5. Binomial Distribution & Discrete Random Variables

Mean, Variance, and Standard Deviation In Exercises 11–14, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

n = 316, p = 0.82

Unusual Events In Exercises 37 and 38, find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.

Rock-Paper-Scissors The probability of winning a game of rock-paper-scissors is 1/3. You play nine games of rock-paper-scissors. Find the probability that the number of games you win is (c) less than two.

Unusual Events In Exercises 37 and 38, find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.

Rock-Paper-Scissors The probability of winning a game of rock-paper-scissors is 1/3. You play nine games of rock-paper-scissors. Find the probability that the number of games you win is (a) exactly five

Unusual Events In Exercises 37 and 38, find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.

Rock-Paper-Scissors The probability of winning a game of rock-paper-scissors is 1/3. You play nine games of rock-paper-scissors. Find the probability that the number of games you win is (b) more than five

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities

Thirty-six percent of Americans think there is still a need for the practice of changing their clocks for Daylight Savings Time. You randomly select seven Americans. Find the probability that the number who say there is still a need for changing their clocks for Daylight Savings Time is (b) less than two

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Living Donor Transplants The mean number of organ transplants from living donors performed per day in the United States in 2020 was about 16. Find the probability that the number of organ transplants from living donors performed on any given day is (a) exactly 12 (Source: Organ Procurement and Transplantation Network)

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Living Donor Transplants The mean number of organ transplants from living donors performed per day in the United States in 2020 was about 16. Find the probability that the number of organ transplants from living donors performed on any given day is (b) at least eight (Source: Organ Procurement and Transplantation Network)

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Living Donor Transplants The mean number of organ transplants from living donors performed per day in the United States in 2020 was about 16. Find the probability that the number of organ transplants from living donors performed on any given day is (c) no more than 10. (Source: Organ Procurement and Transplantation Network)

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Oil Tankers In the month of June 2021, 240 oil tankers stop at a port city. No oil tanker visits more than once. Find the probability that the number of oil tankers that stop on any given day in June is (a) exactly eight

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Oil Tankers In the month of June 2021, 240 oil tankers stop at a port city. No oil tanker visits more than once. Find the probability that the number of oil tankers that stop on any given day in June is (b) at most three

Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Oil Tankers In the month of June 2021, 240 oil tankers stop at a port city. No oil tanker visits more than once. Find the probability that the number of oil tankers that stop on any given day in June is (c) more than eight.

An auto parts seller finds that 1 in every 200 parts sold is defective. Use the geometric distribution to find the probability that (c) none of the first 20 parts sold are defective.

Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Responsible Consumption Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 16 consumers. Find the probability that the number of of consumers who say it is important that the clothing they buy is made without child labor is (a) e

Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Penalty Kicks Argentine soccer player Lionel Messi converts 78% of his penalty kicks. Suppose Messi takes six penalty kicks next season. Find the probability that the number he converts is (a) exactly six, (b) at most three, and (c) more than three. (Source: Transfermarkt)

Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Civil Rights Fifty-nine percent of U.S. adults think that civil rights for Black Americans have improved during their lifetime. You randomly select seven U.S. adults. Find the probability that the number who think that civil rights for Black Americans have improved during their lifetime is (a) exactly one and (b) exactly five. (Source: Gallup)