MATH 302 WEEK 3 TEST QUESTIONS & ANSWERS | 2022 latest update | 100% correct

MATH 302 WEEK 3 TEST A coin is flipped 30 times. Find σ². Round to 1 decimal place. Answer: 7.5 30*.5*.5 Question 2 1 / 1 point Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer: 20 200*.10 Question 3 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the P(X ≤ 3) using Excel. Round answer to 4 decimal places. Answer: 0.9021 In Excel, =BINOM.DIST(3,14,0.13,TRUE) Question 4 1 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 5 adult workers is selected, what is the probability that more than 3 of them have a high school diploma? (That is, what is P(X>3) (round to 4 decimal places) Answer: 0.1875 P(x > 3) = 1 - P(x ≤ 3), in Excel =1-BINOM.DIST(3,5,0.5,TRUE) Question 5 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the P(X = 15) using Excel. Round answer to 4 decimal places. Answer: 0.0016 In Excel, =BINOM.DIST(15,25,0.85,FALSE) Question 6 1 / 1 point The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2,873 Jackie Robinson 1,054 273 54 137 1,518 Ty Cobb 3,603 174 295 114 4,186 Hank Aaron 2,294 624 98 755 3,771 TOTALS 8,468 1,577 583 1,720 12,351 Find P(hit was a Home Run|The hit was made by Ty Cobb ). Question options: 0.009 0.066 0.027 0.973 114/4186 Question 7 1 / 1 point A baseball team has a 20-person roster. A batting order has nine people. How many different batting orders are there? Answer: Question options: 00 800 Order Matters =PERMUT(20,9) Order Matters =PERMUT(20,9) Question 8 1 / 1 point Find the probability of rolling a sum of two dice that is a 7 or a 12. Round answer to 4 decimal places. Answer: 0.1944 Dice outcomes 1 1 2 3 4 5 6 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) 2 3 4 5 6 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Only 7 ways to sum to exactly 7 or exactly 12 7/36 Question 9 1 / 1 point The number of M&M's for each color found in a case were recorded in the table below. Blue = 481, Brown = 371, Green = 483, Orange = 544, Red = 372, Yellow = 369 Total = 2620 What is the probability of selecting a red M&M? Round answer to 4 decimal places. Answer: 0.1420 372/2620 Question 10 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 46% 28% 26% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Answer: 0.54 (round to 2 decimal places) .28 + .26 Question 11 1 / 1 point The random variable X = the number of vehicles owned. Find the probability that a person owns less than 2 vehicles. Round to two decimal places. x 0 1 2 3 4 P(X=x) 0.1 0.35 0.25 0.2 0.1 Answer: 0.45 Less than 2 is P(x = 0) + P(x = 1) .1 + .35 Question 12 1 / 1 point Does the following table represent a valid discrete probability distribution? x -5 -2.5 0 2.5 5 P(X= x) 0.05 0.25 0.32 0.18 0.2 Question options: yes no Yes, because the probabilities add up to 1 Question 13 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 55% 28% 17% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Answer: 0.45 (round to 2 decimal places) .28 + . 17 Question 14 0 / 1 point There are on average 5 old growth Sitka Spruce trees per 1/8 of an acre in a local forest. Find the probability that that there are exactly 30 Sitka Spruce trees in 1 acre in a remote part of the forest that is scheduled to be logged next year. Round answer to 4 decimal places. Answer: .3689 New mean per 1 acre = 5*8= 40. P(x = 30), in Excel =POISSON.DIST(30,40,FALSE) Question 15 0 / 1 point A bank gets an average of 11 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or more customers at this bank in one hour. (That is, find P(X ≥ 9)) (round to 4 decimal places) Answer: 0.1189 Hide Feedback P(X≥9) = 1 - P(x ≤ 8), in Excel =1-POISSON.DIST(8,11,TRUE) Question 16 0 / 1 point The number of rescue calls received by a rescue squad in a city follows a Poisson distribution with an average of 2.83 rescues every eight hours. What is the probability that the squad will have at most 2 calls in an hour? Round answer to 4 decimal places. Answer: .1126 Hide Feedback New mean = 2.83/8 = .35375 per hour. P(x ≤ 2), in Excel =POISSON.DIST(2,0.35375,TRUE) Question 17 0 / 1 point The mean number of visitors at a national park in one weekend is 52. Assume the variable follows a Poisson distribution. Find the probability that there will be 58 visitors at this park in one weekend. (That is, find P(X=58) (Round answer to 4 decimal places) Answer: .5556 Hide Feedback In Excel, =POISSON.DIST(58,52,FALSE) Question 18 0 / 1 point A bank gets an average of 8 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 customers at this bank in one hour. (That is, find P(X=11) (Round answer to 4 decimal places) Answer: .8962 Hide Feedback In Excel, =POISSON.DIST(11,8,FALSE) Question 19 1 / 1 point A drug is reported to benefit 40% of the patients who take it. If 6 patients take the drug, what is the probability that 4 or more patients will benefit? Question options: 0.138 Hide Feedback P(x 4) = 1 - P(x 3), in Excel =1- BINOM.DIST(3,6,0.4,TRUE) Question 20 0 / 1 point You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area. Let B = the event of landing on blue. Let R = the event of landing on red. Let G = the event of landing on green. Let Y = the event of landing on yellow. If you land on Y, you get the grand prize. Find P(Y). Question options: 0.18 0.125 0.25 0.8 Hide Feedback 1 Yellow piece, 1/8 1 Yellow piece, 1/8 Question 1 1 / 1 point Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that at most 2 of them have blue eyes? Round answer to 4 decimal places. Answer: 0.7879 Hide Feedback P(x ≤ 2), in Excel =BINOM.DIST(2,20,0.08,TRUE) Question 2 1 / 1 point It is known that 40% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the expected number of adult workers with a high school diploma? (That is, what is E(X)?) Round to the whole number. Do not use decimals. Answer: 4 Hide Feedback 10*.4 Question 3 1 / 1 point If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer: 9 Hide Feedback 15*.6 Question 4 1 / 1 point If random variable X has a binomial distribution with n =10 and P(success) = p =0.6, find the probability that X is more than 3. (That is, find P(X>3) (round to 4 decimal places) Answer: 0.9452 Hide Feedback P(x > 3) = 1 - P(x ≤3) , in Excel =1-BINOM.DIST(3,10,0.6,TRUE) Question 5 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the standard deviation. Round answer to 4 decimal places. Answer: 1.2583 Hide Feedback In Excel, =SQRT(14*0.13*0.87) Question 6 1 / 1 point The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2,873 NAME Single Double Triple Home Run TOTAL HITS Jackie Robinson 1,054 273 54 137 1,518 Ty Cobb 3,603 174 295 114 4,189 Hank Aaron 2,294 624 98 755 3,771 TOTALS 8,468 1,577 583 1,720 12,351 Find P(hit was made by Hank Arron|The hit was a Single). Question options: 0.066 0.729 0.271 0.033 Hide Feedback 2294/8468 Question 7 1 / 1 point The California license plate has one number followed by three letters followed by three numbers. How many different license plates are possible? Do not use commas in your answer. Answer: Hide Feedback 1 * 263 * 103 Question 8 1 / 1 point In a box there are 3 red cards and 5 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a red card? (round to 3 decimal places) Answer: 0.375 Hide Feedback 3/8 Question 9 1 / 1 point In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. Find the probability of winning if you pick the number 30 and it comes up on the wheel. Round your answer to 3 decimal places. Answer: 0.026 Hide Feedback There is only 1 way to land on 30 and there are 38 total possibilities. 1/38 Question 10 0 / 1 point The random variable X = the number of vehicles owned. Find the expected number of vehicles owned. Round answer to two decimal places. Number of Courses , x 0 1 2 3 4 Probability, P(X=x) 0.2 0.35 0.25 0.1 0.1 Answer: 1.85 Hide Feedback 0*.2 + 1*.35 + 2*.25 + 3*.1 + 4*.1 Question 11 1 / 1 point Is the following table a valid discrete probability distribution? x -5 -2.5 0 2.5 5 P(X=x) 0.15 0.25 0.32 0.18 0.1 Question options: No, since the probabilities do not add up to 1. Yes, since all the probabilities are between 0 and 1 and the probabilities add up to one. No, since not all the values are between 0 and 1. Question 12 Yes, since all the x values add up to 0. 1 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.11 0.06 0.25 0.41 0.51 Question options: yes no Hide Feedback No, since the probabilities do not add up to 1 Question 13 1 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.16 0.01 0.25 0.11 0.66 Question options: Yes No Hide Feedback No, since the probabilities do not add up to 1 Question 14 1 / 1 point Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. What is the probability that the company will receive 3 calls in a 12 minute period? Round answer to 4 decimal places. Answer: 0.2225 Hide Feedback New Mean = 14/60 = .23333 per hour. For 12 hours 12*.. P(x = 3), in Excel =POISSON.DIST(3,2.8,FALSE) Question 15 1 / 1 point A coffee shop serves an average of 75 customers per hour during the morning rush. Find the probability that 80 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places. Answer: 0.0379 Hide Feedback P(x = 80), in Excel =POISSON.DIST(80,75,FALSE) Question 16 1 / 1 point The mean number of visitors at a national park in one weekend is 47. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 55 visitors at this park in one weekend. (That is, find P(X ≤ 55)) (round to 4 decimal places) Answer: 0.8904 Hide Feedback In Excel, =POISSON.DIST(55,47,TRUE) Question 17 0 / 1 point If random variable X has a Poisson distribution with mean = 4.5, find the probability that X is more than 8. (That is, find P(X>8) (round to 4 decimal places) Answer: 0.0866 Hide Feedback P(x > 8) = 1 - P(x ≤ 8), in Excel =1-POISSON.DIST(8,4.5,TRUE) Question 18 1 / 1 point There are 6.5 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or less accidents at this intersection. (That is, find P(X≤9) (round to 4 decimal places) Answer: 0.8774 Hide Feedback In Excel, =POISSON.DIST(9,6.5,TRUE) Question 19 0 / 1 point The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains 38 numbers, and each number is assigned to a color and a range. What is the probability of winning when betting on two lines that touch each other on the table as in 1-2-3-4- 5-6? Question options: 4/38 5/38 6/38 2/38 Hide Feedback 6 chances to win out of 38 possibilities. Question 20 1 / 1 point A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and 5 bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(N). Question options: 0.13 0.12 0.36 0.24 Hide Feedback 15/42 Question 1 0 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 6 adult workers is selected, what is the probability that 3 or more of them have a high school diploma? (That is, find P(X ≤ 3) (round to 4 decimal places) Answer: 3) (round to 4 decimal places) Answer: 0.6875 Hide Feedback P(X ≥ 3) = 1 - P(x ≤ 2), in Excel =1-BINOM.DIST(2,6,0.5,TRUE) Question 2 1 / 1 point Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer: 0.2711 Hide Feedback P(x = 2), in Excel, =BINOM.DIST(2,20,0.08,FALSE) Question 3 1 / 1 point If random variable X has a binomial distribution with n =10 and P(success) =p =0.2, find the probability that X is less than 6. (That is, find P(X<6) Answer: (round to 4 decimal places) 0.9936 Hide Feedback P(x < 6) = P(x ≤ 5) , in Excel Question 4 1 / 1 point Approximately 10% find of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer: 20 Hide Feedback 200*.10 Question 5 1 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 5 adult workers is selected, what is the probability that more than 3 of them have a high school diploma? (That is, what is P(X>3) (round to 4 decimal places) Answer: 0.1875 Hide Feedback P(x > 3) = 1 - P(x ≤ 3), in Excel =1-BINOM.DIST(3,5,0.5,TRUE) Question 6 1 / 1 point The table shows a random sample of musicians and how they learned to play their instruments. Gender Self-Taught Studied in School Private Instruction Total Female 12 38 22 72 Male 19 24 15 58 Total 31 62 37 130 Find P(musician is a female AND had private instruction). Question options: 0.17 0.12 0.88 0.83 Hide Feedback 22/130 Question 7 1 / 1 point There are 4 answers for a single question on the exam and only one answer is correct. If a student guesses the answer for this question, what is the probability that the student selects the correct answer? (round to 2 decimal places) Answer: 0.25 Hide Feedback 4 possibilities but only 1 correct answer. 1/4 Question 8 1 / 1 point How many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1? Do not use commas in your answer. Answer: Hide Feedback First number has 8 different choice then the last 6 numbers can be any number. 8 * 106 Question 9 1 / 1 point In a box there are 3 red cards and 5 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a red card? (round to 3 decimal places) Answer: 0.375 Hide Feedback 3/8 Question 10 1 / 1 point The random variable X = the number of vehicles owned. Find the P(X > 2). Round to two decimal places. x 0 1 2 3 4 P(X=x) 0.1 0.35 0.25 0.2 0.1 Answer: 0.30 Hide Feedback Greater than 2, is P(x = 3) + P(x = 4) .2 + .1 Question 11 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 46% 28% 26% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Answer: 0.54 (round to 2 decimal places) Hide Feedback .28 + .26 Question 12 1 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.16 0.01 0.25 0.11 0.66 Question options: Yes No Hide Feedback No, since the probabilities do not add up to 1 Question 13 1 / 1 point The random variable X = the number of vehicles owned. Find the probability that a person owns less than 2 vehicles. Round to two decimal places. x 0 1 2 3 4 P(X=x) 0.1 0.35 0.25 0.2 0.1 Answer: 0.45 Hide Feedback Less than 2 is P(x = 0) + P(x = 1) .1 + .35 Question 14 1 / 1 point If random variable X has a Poisson distribution with mean = 7, find the probability that X is more than 8. (That is, find P(X>8) (round to 4 decimal places) Answer: 0.2709 Hide Feedback P(x > 8) = 1- P(x ≤ 8), in Excel =1-POISSON.DIST(8,7,TRUE) Question 15 1 / 1 point A bank gets an average of 15 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 or more customers at this bank in one hour. (That is, find P(X ≥ 11) (round to 4 decimal places) Answer: 0.8815 Hide Feedback P(X≥11) = 1 - P(x ≤ 10), in Excel =1-POISSON.DIST(10,15,TRUE) Question 16 1 / 1 point A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 10 or more customers at this bank in one hour. (That is, find P(X≥10) (round to 4 decimal places) Answer: 0.7576 Hide Feedback P(X≥10) = 1 - P(x ≤ 9), in Excel =1-POISSON.DIST(9,12,TRUE) Question 17 1 / 1 point Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. Assume the variable follows a Poisson distribution. What is the probability that the company will receive more than 20 calls per hour? Round answer to 4 decimal places. Answer: 0.0479 Hide Feedback P(x > 20) = 1 - P(x ≤ 20). In Excel, =1-POISSON.DIST(20,14,TRUE) Question 18 0 / 1 point There are 4 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 5 or less accidents at this intersection. (That is, find P(X ≤ 5)) (round to 4 decimal places) Answer: 0.7876 Hide Feedback In Excel, =POISSON.DIST(5,4,TRUE) Question 19 1 / 1 point A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange. Let B = the event of getting a blue jelly bean Let G = the event of getting a green jelly bean. Let O = the event of getting an orange jelly bean. Let P = the event of getting a purple jelly bean. Let R = the event of getting a red jelly bean. Let Y = the event of getting a yellow jelly bean. Find P(R) Question options: 0.12 0.11 0.15 0.13 Hide Feedback 22/150 Question 20 0 / 1 point What type of probability uses sample spaces to determine the numerical probability that an event will occur? Question options: subjective probability empirical probability classical probability conditional probability Quiz Submissions - Week 3 Test Justin May (username: ) Attempt 1 Written: Jan 19, 2021 4:35 PM - Jan 19, 2021 5:35 PM Submission View Your quiz has been submitted successfully. Question 1 1 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma? (That is, what is P(X < 6) (round to 4 decimal places) Answer: 0.8555 Hide Feedback P(x < 6) = P(x ≤ 5), in Excel =BINOM.DIST(5,8,0.5,TRUE) Question 2 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the variance. Round answer to 4 decimal places. Answer: 3.1875 Hide Feedback 25*.85*.15 Question 3 0 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the P(X = 3) using Excel. Round answer to 4 decimal places. Answer: 0.9021 Hide Feedback In Excel, =BINOM.DIST(3,14,0.13,FALSE) Question 4 1 / 1 point Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find μ. Round to one decimal place. Answer: 1.6 Hide Feedback 20*.08 Question 5 1 / 1 point A coin is flipped 30 times. What is the probability of getting exactly 15 heads? Round answer to 4 decimal places. Answer: 0.1445 Hide Feedback P(x = 15), in Excel, =BINOM.DIST(15,30,0.5,FALSE) Question 6 1 / 1 point The table shows a random sample of musicians and how they learned to play their instruments. Gender Self-Taught Studied in School Private Instruction Total Female 12 38 22 72 Male 19 24 15 58 Total 31 62 37 130 Find P(musician is a female AND had self taught). Question options: 0.12 0.09 0.91 0.29 Hide Feedback 12/130 Question 7 0 / 1 point How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type? Leave answer a whole number, do not include decimals or commas. Answer: Hide Feedback Order does not matter. In Excel, =COMBIN(25,4) Question 8 1 / 1 point An experiment is to flip a fair coin three times. What is the probability of getting exactly two heads? Round to 3 decimal places. Answer: 0.375 Hide Feedback TTT TTH THT HTT HHH HHT HTH THH Exactly 2 Heads happens 3 times. Probability = 3/8 Question 9 1 / 1 point A raffle sells 1000 tickets for $35 each to win a new car. What is the probability of winning the car? Round to three decimal places. Answer: 0.001 Hide Feedback Only 1 person will win the car Probability = 1/1000 Question 10 1 / 1 point Is the following table a valid discrete probability distribution? x 0 1 2 3 4 P(X=x) 0.111 0.214 0.312 0.163 0.159 Question options: Yes, since all the x values are greater than 0. No, since the probabilities do not add up to 1. No, since not all the probabilities are between 0 and 1. Yes, since all the probabilities are between 0 and 1 and the probabilities add up to one. Hide Feedback Probability always need to add up to 1 or 100% Question 11 1 / 1 point True or False: The following table represents a valid discrete probability distribution. x 1 2 3 4 5 P(X=x) 0.16 0.06 0.05 0.21 0.01 Question options: True False Hide Feedback The probabilities need to add up to 1 or 100% Question 12 1 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.11 0.06 0.18 0.06 0.96 Question options: yes no Hide Feedback No, since the probabilities do not add up to 1 Question 13 1 / 1 point A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years. Complete Table using the data provided. Round to two decimal places. x P(x) 0 0.12 1 0.18 2 0.30 3 0.15 4 5 0.10 6 0.05 0.10 Hide Feedback 1 - (.12 + .18 +.30 + .15+ .10 + .05) 1 - .90 Question 14 0 / 1 point If random variable X has a Poisson distribution with mean = 10, find the probability that X is at least 2. (That is, find P(X ≥ 2) (round to 4 decimal places) 0.9973 Hide Feedback P(x ≥ 2) = 1 - P(x ≤ 1) , in Excel =1-POISSON.DIST(1,10,TRUE) Question 15 0 / 1 point There are 4 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be less than 2 accidents at this intersection. (That is, find P(X < 2)) (round to 4 decimal places) Answer: 0.1465 Hide Feedback P(x < 2) = P(x ≤ 1), in Excel =POISSON.DIST(1,4,TRUE) Question 16 1 / 1 point The mean number of visitors at a national park in one weekend is 55. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 71 visitors at this park in one weekend. (That is, find P(X≤71) (round to 4 decimal places) Answer: 0.9841 Hide Feedback In Excel, =POISSON.DIST(71,55,TRUE) Question 17 1 / 1 point If random variable X has a Poisson distribution with mean = 6, find the probability that X is 12. (That is, find P(X=12) (Round answer to 4 decimal places) Answer: 0.0113 Hide Feedback In Excel, =POISSON.DIST(12,6,FALSE) Question 18 1 / 1 point Suppose a random variable, x, follows a Poisson distribution. Let µ=2.5 every minute, find the P(X=125) over an hour. Round answer to 4 decimal places. Answer: .0039 Hide Feedback New mean per hour is 2.5*60 = 150 In Excel, =POISSON.DIST(125,150,FALSE) Question 19 1 / 1 point A furniture manufacturer offers bookcases in 6 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is: Question options: 9 18 15 6 Hide Feedback 6*3 Question 20 1 / 1 point The table below shows the preferences for elective courses of students who are undecided about their majors. Philosophy Digital Art Film Studies Male 9 16 22 Female 6 18 14 What is the probability of randomly selecting a student who is female or prefers Digital Art? Question options: 46.2% 84.7% 63.5% 21.2% Hide Feedback P(F or DA) = P(F) + P(DA) - P(F and DA) (38/85)+(34/85) - (18/85) Attempt Score: 16 / 20 - 80 % Overall Grade (highest attempt): 16 / 20 - 80 % Question 1 1 / 1 point An unprepared student takes a 10 question TRUE/FALSE quiz and ended up guessing on all the problems. Find σ. Round answer to 4 decimal places. Answer: 1.5811 Hide Feedback In Excel, =BINOM.DIST(3,8,0.5,TRUE) Question 2 1 / 1 point Approximately 10% of all people are left-handed. Out of a random sample of 15 people, what is the probability that 4 of them are left-handed? Round answer to 4 decimal places. Answer: 0.0428 Hide Feedback P(x = 4), In Excel, =BINOM.DIST(4,15,0.1,FALSE) Question 3 0 / 1 point If random variable X has a binomial distribution with n =7 and P(success) = p =0.6, find the probability that X is at least 6. (That is, find P(X ≥ 6) (round to 4 decimal places) Answer: 0.0280 Hide Feedback P(x ≥ 6) = 1 - P(x ≤ 5), in Excel =1-BINOM.DIST(5,7,0.6,TRUE) Question 4 0 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the P(X ≥ 15) using Excel. Round answer to 4 decimal places. Answer: 0.9979 Hide Feedback P(x ≥ 15)= 1 - P(x ≤ 14), in Excel =1-BINOM.DIST(14,25,0.85,TRUE) Question 5 0 / 1 point It was found that 60% of people have a dog as a pet. If a random sample of 11 people is selected, what is the variance of the number of people that have a dog as a pet? (That is, what is Var(X)?) (round to 2 decimal places) Answer: 6.6 Hide Feedback =11*0.6*0.4 Question 6 1 / 1 point The table shows a random sample of musicians and how they learned to play their instruments. Gender Self-Taught Studied in School Private Instruction Total Female 12 38 22 72 Male 19 24 15 58 Total 31 62 37 130 Find P(musician is a male AND had private instruction). Question options: 0.71 0.12 0.88 0.29 Hide Feedback Good job, 15/130 Question 7 0 / 1 point You have a club of fifteen people. You need to pick a president, treasurer, and secretary from the fifteen. How many different ways can you do this? Leave answer as whole number, do not include decimals or commas. Answer: 2300 Hide Feedback Order matters. In Excel, =PERMUT(15,3) Question 8 1 / 1 point In a box there are 4 red cards and 7 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a blue card? (round to 3 decimal places) Answer: 0.636 Hide Feedback Probability = 7/11 Question 9 1 / 1 point You are opening a T-shirt store. You can have long sleeves or short sleeves, three different colors, five different designs, and four different sizes. How many different shirts can you make? Leave answer as a whole number, do not include decimals. Answer: 120 Hide Feedback 3*5*4 = 60 Long or short sleeve = 2*60 Question 10 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses , x 1 2 3 Probability, P(X=x) 52% 28% 20% What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2) Answer: 0.48 (round to 2 decimal places) Hide Feedback Greater than or equal to 2 is 2 AND 3. P(x =2) + P(x = 3) .28 + .20 Question 11 1 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.16 0.11 0.06 - 0.36 0.21 Question options: yes no Hide Feedback No, since the probabilities do not add up to 1 and all probabilities need to be between 0 and 1. Probabilities cannot be negative. Question 12 0 / 1 point Does the following table represent a valid discrete probability distribution? x 1 2 3 4 5 P(X= x) 0.11 0.06 0.18 0.06 0.59 Question options: yes no Hide Feedback Yes, because the probabilities add up to 1. Question 13 0 / 1 point The random variable X = the number of vehicles owned. Find the probability that a person owns at least 2 vehicles. Round to two decimal places. x 0 1 2 3 4 P(X=x) 0.1 0.35 0.25 0.2 0.1 Answer: 55 Hide Feedback At least 2 vehicles is the probability of P(x = 2) + P(x = 3) + P(4) .25 +.2 + .1 Question 14 1 / 1 point If random variable X has a Poisson distribution with mean = 4.5 find the probability that X is more than 4. (That is, find P(X>4) (round to 4 decimal places) Answer: 0.4679 Hide Feedback P(x > 4) = 1 - P(x ≤ 4) , in Excel =1-POISSON.DIST(4,4.5,TRUE) Question 15 1 / 1 point There are 3.1 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 5 accidents at this intersection. (That is, find P(X=5) (Round answer to 4 decimal places) Answer: 0.1075 Hide Feedback In Excel, =POISSON.DIST(5,3.1,FALSE) Question 16 1 / 1 point There are on average 20 old growth Sitka Spruce trees per acre in a local forest. Find the probability that that there are more than 8 Sitka Spruce trees in a ¼ acre. Round answer to 4 decimal places. Answer: 0.0681 Hide Feedback New mean per 1/4 acre = 20/4 = 5. P(x > 8) = 1 - P(x ≤ 8), in Excel =1-POISSON.DIST(8,5,TRUE) Question 17 1 / 1 point Suppose a random variable, x, follows a Poisson distribution. Let μ = 2.5 every minute, find the P(X ≥ 125) over an hour. Round answer to 4 decimal places. Answer: 0.9835 Hide Feedback New mean per hour = 2.5*60 = 150. P(x ≥ 125) = 1 - P(x ≤ 124) , in Excel =1-POISSON.DIST(124,150,TRUE) Question 18 1 / 1 point The mean number of visitors at a national park in one weekend is 55. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 49 visitors at this park in one weekend. (That is, find P(X≤49)) (round to 4 decimal places) Answer: 0.2322 Hide Feedback In Excel, =POISSON.DIST(49,55,TRUE) Question 19 1 / 1 point United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any bloodtype. Their data shows that 43% of people have type O blood and 15% of people have Rh- factor; 52% of people have type O or Rh- factor. Find the probability that a person has both type O blood and the Rh- factor. Question options: 5% of people have type O, Rh- blood 33% of people have type O, Rh- blood 6% of people have type O, Rh- blood 94% of people have type O, Rh- blood Hide Feedback P(O or Rh-) = P(O) + P(Rh-) - P(O and Rh-) .52 = .43 + .15 - P(O and Rh-) .52 = .58 - P(O and Rh-) Question 20 1 / 1 point In a recent study, the following data were obtained in response to the question, "Do you favor recycling in your neighborhood?" Yes No No Opinion Males 25 15 10 Females 30 10 10 If a person is picked at random, what is the probability that the person is either male or has no opinion regarding recycling? Question options: 3/10 3/5 7/10 4/5 Hide Feedback P(M or No) = P(M) + P(No) - P(M and No) (50/100) + (20/100) - (10/100)