MATH302 Week 3 Test

1. Question: A coin is flipped 30 times. What is the probability of getting 15 or more heads? Round answer to 4 decimal places. 2. Question: 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? 3. Question: If random variable X has a binomial distribution with n=9 and P(success) =p= 0.4, find the standard deviation of X. 4. Question: If random variable X has a binomial distribution with n =8 and P(success) = p =0.5, find the probability that X is at most 3. 5. Question: 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. 6. Question: The table shows a random sample of musicians and how they learned to play their instruments. Find P(musician is a female AND had self taught). 7. Question: 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. 8. Question: You are going to a benefit dinner, and need to decide before the dinner what you want for salad, main dish, and dessert. You have 2 different salads to choose from, 3 main dishes, and 5 desserts. How many different meals are available? 9. Question: 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? 10. Question: 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. 11. Question: Does the following table represent a valid discrete probability distribution? 12. Question: Is the following table a valid discrete probability distribution? 13. Question: The random variable X = the number of vehicles owned. Find the standard deviation of the number of vehicles owned. Round answer to 4 decimal places. 14. Question: 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. 15. Question: 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. 16. Question: If random variable X has a Poisson distribution with mean = 10, find the probability that X is at least 2. 17. Question: 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. 18. Question: 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. 19. Question: In a particular college class, there are male and female students. Some students have long hair and some students have short hair. Let F be the event that a student identifies as female. Let M be the event that a student identifies as male. Let S be the event that a student has short hair. Let L be the event that a student has long hair. Choose the best fit symbols for the event identified below. The probability that a student identifies as male, given that the student has long hair. 20. Question: In a recent study, the following data were obtained in response to the question, "Do you favor recycling in your neighborhood?"