4.2 Binomial Distributions

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the test?

0.055

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that at least eight were married?

0.167

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that two or fewer were never married?

0.167

Fifty percent of the people that get mail-order catalogs order something. Find the probability that exactly three of 10 people getting these catalogs will order something.

0.117

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three boys in ten births.

0.172

According to police sources, a car with a certain protection system will be recovered 90% of the time. Find the probability that 5 of 10 stolen cars will be recovered.

0.001

A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test?

0.006

The probability that a tennis set will go to a tie-breaker is 11%. What is the probability that two of three sets will go to tie-breakers?

0.032

Sixty-five percent of men consider themselves knowledgeable football fans. If 13 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans.

0.034

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly eight boys in ten births.

0.044

The probability that an individual is left-handed is 0.17. In a class of 55 students, what is the probability of finding five left-handers?

0.044

In a recent survey, 76% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.

0.064

A test consists of 110 true or false questions. If the student guesses on each question, what is the mean number of correct answers?

55

Find the standard deviation of the binomial distribution for which n = 400 and p = 0.86.

6.94

A test consists of 290 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?

8.51

According to police sources, a car with a certain protection system will be recovered 92% of the time. If 800 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen?

mean: 736; standard deviation: 7.67

Find the variance of the binomial distribution for which n = 400 and p = 0.94.

22.56

In one city, 29% of adults smoke. In groups of size 120 of adults, what is the variance of the number that smoke ?

24.71

The probability that a house in an urban area will be burglarized is 3%. If 22 houses are randomly selected, what is the probability that none of the houses will be burglarized?

0.512

A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over 50, what is the probability that at least six wear glasses?

0.850

The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, what is the mean of the number of houses burglarized?

1

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?

1.55

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

12

Find the mean of the binomial distribution for which n = 80 and p = 0.2.

16

A test consists of 10 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.

mean: 2; standard deviation: 1.26

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the mean and standard deviation of the number that never married?

mean: 4; standard deviation: 1.55

The probability that a tennis set will go to a tiebreaker is 14%. In 420 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers?

mean: 58.8; standard deviation: 7.11

A recent survey found that 64% of all adults over 50 wear glasses for driving. In a random sample of 100 adults over 50, what is the mean and standard deviation of those that wear glasses?

mean: 64; standard deviation: 4.8

The probability that an individual is left-handed is 0.15. In a class of 50 students, what is the mean and standard deviation of the number of left-handers in the class?

mean: 7.5; standard deviation: 2.52