MATH STATISTICS - Review 2 CH 4-6 SHOW WORK FOR FULL CREDIT
Name___________________________________
Find the indicated probability.
1) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles.
a) If a marble is randomly selected from the bag, what is the probability that it is blue?
b) If a marble is randomly selected what is the probability it is red?
c) If two marbles are selected what is the probability both are green? (with replacment)
d) If two marbles are selected what is the prob the first is red and second is green? (with replacment)
e) If two marbles are selected what is the prob the first is red and second is green? (without replacment)
2) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker smoker smoker smoker Total
Men 334 50 68 32 484
Women 357 30 89 37 513
Total 691 80 157 69 997
a) If one of the 997 people is randomly selected, find the probability of getting a regular or heavy smoker.
b) What is the probability a person is a heavy smoker and male.
3) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker smoker smoker smoker Total
Men 431 50 71 49 601
Women 382 48 86 39 555
Total 813 98 157 88 1156
a) If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy
smoker.
b) What is the probability a person is an occasional smoker given they are a women?
4) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men 390 34 42 466
Women 446 35 44 525
Total 836 69 86 991
If two different people are randomly selected from the 991 subjects, find the probability that they are both
heavy smokers. Treat as dependent events. Round to six decimal places.
5) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men 425 38 35 498
Women 381 32 43 456
Total 806 70 78 954
If two different people are randomly selected from the 954 subjects, find the probability that they are both
women. Without replacment. Round to four decimal places.
1
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, 6) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when
two coils are randomly selected if the first selection is replaced before the second is made.
7) A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin.
Treat as independent. Find the probability that all the bulbs selected are good ones. Round to the nearest
thousandth if necessary.
8) A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the
probability that she selects none of those containing errors? Round to four decimal places.
Provide an appropriate response.
9) Mutually exclusive (or disjoint) events are events that cannot occure at the same time.
a) Give an example of b) Give an example of events
mutually excusive events that are not mutually exclusive
10) Independent events are events where the outcome of one does not affect the other. If events are not
independent then they are dependent.
a) Give an example b) Give an example of
independent events . dependent events.
Find the indicated binomial probability.
11) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at
random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?
12) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly.
If a student guesses on each question, what is the probability that the student will pass the test?
13) A tennis player makes a successful first serve 51% of the time. Assuming that each serve is independent of
the others. If she serves 9 times,
a) what is the probability that she gets exactly 3 first serves in?
b) what is the probability that she gets more than 3 first serves in?
c) what is the probability that she gets at least 3 first serves in?
d) what is the probability that she gets at most 3 first serves in?
e) what is the probability that she gets fewer than 3 first serves in?
Solve the problem. graph, shade and label the normal distribution.
14) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109
inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation
during 25 randomly picked years will be less than 111.8 inches?
15) The scores on a certain test are normally distributed with a mean score of 60 and a standard deviation of 5.
What is the probability that a sample of 90 students will have a mean score of at least 60.527?
16) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104
inches, and a standard deviation of 10 inches.
a) If one year is selected at random what is the probability the annual precipitation will be less than 106.8?
b) What is the probability that the mean annual precipitation during 25 randomly picked years will be less
than 106.8 inches?
2
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Name___________________________________
Find the indicated probability.
1) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles.
a) If a marble is randomly selected from the bag, what is the probability that it is blue?
b) If a marble is randomly selected what is the probability it is red?
c) If two marbles are selected what is the probability both are green? (with replacment)
d) If two marbles are selected what is the prob the first is red and second is green? (with replacment)
e) If two marbles are selected what is the prob the first is red and second is green? (without replacment)
2) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker smoker smoker smoker Total
Men 334 50 68 32 484
Women 357 30 89 37 513
Total 691 80 157 69 997
a) If one of the 997 people is randomly selected, find the probability of getting a regular or heavy smoker.
b) What is the probability a person is a heavy smoker and male.
3) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker smoker smoker smoker Total
Men 431 50 71 49 601
Women 382 48 86 39 555
Total 813 98 157 88 1156
a) If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy
smoker.
b) What is the probability a person is an occasional smoker given they are a women?
4) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men 390 34 42 466
Women 446 35 44 525
Total 836 69 86 991
If two different people are randomly selected from the 991 subjects, find the probability that they are both
heavy smokers. Treat as dependent events. Round to six decimal places.
5) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men 425 38 35 498
Women 381 32 43 456
Total 806 70 78 954
If two different people are randomly selected from the 954 subjects, find the probability that they are both
women. Without replacment. Round to four decimal places.
1
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, 6) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when
two coils are randomly selected if the first selection is replaced before the second is made.
7) A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin.
Treat as independent. Find the probability that all the bulbs selected are good ones. Round to the nearest
thousandth if necessary.
8) A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the
probability that she selects none of those containing errors? Round to four decimal places.
Provide an appropriate response.
9) Mutually exclusive (or disjoint) events are events that cannot occure at the same time.
a) Give an example of b) Give an example of events
mutually excusive events that are not mutually exclusive
10) Independent events are events where the outcome of one does not affect the other. If events are not
independent then they are dependent.
a) Give an example b) Give an example of
independent events . dependent events.
Find the indicated binomial probability.
11) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at
random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?
12) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly.
If a student guesses on each question, what is the probability that the student will pass the test?
13) A tennis player makes a successful first serve 51% of the time. Assuming that each serve is independent of
the others. If she serves 9 times,
a) what is the probability that she gets exactly 3 first serves in?
b) what is the probability that she gets more than 3 first serves in?
c) what is the probability that she gets at least 3 first serves in?
d) what is the probability that she gets at most 3 first serves in?
e) what is the probability that she gets fewer than 3 first serves in?
Solve the problem. graph, shade and label the normal distribution.
14) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109
inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation
during 25 randomly picked years will be less than 111.8 inches?
15) The scores on a certain test are normally distributed with a mean score of 60 and a standard deviation of 5.
What is the probability that a sample of 90 students will have a mean score of at least 60.527?
16) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104
inches, and a standard deviation of 10 inches.
a) If one year is selected at random what is the probability the annual precipitation will be less than 106.8?
b) What is the probability that the mean annual precipitation during 25 randomly picked years will be less
than 106.8 inches?
2
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