21. Basic Computation: p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = bution by a normal distribution? Why? Compute Mp and op. (b) Suppose n = tion by a normal distribution? Why or why not? 100 and p = 0.23. Can we safely approximate the p distri- 20 and p = 0.23. Can we safely approximate the p distribu-
21. Basic Computation: p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = bution by a normal distribution? Why? Compute Mp and op. (b) Suppose n = tion by a normal distribution? Why or why not? 100 and p = 0.23. Can we safely approximate the p distri- 20 and p = 0.23. Can we safely approximate the p distribu-
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**15.** The airline knows from past experience that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation will show up for the flight?
(b) Let \( n = 267 \) represent the number of ticket reservations. Let \( r \) represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation?
\[ P(255 \leq r); \, P(r \leq 255); \, P(r \leq 267); \, P(r = 255) \]
(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation?
**16. General: Approximations** We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which you discuss and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions made for each approximation. Give details and examples in your essay. How could you apply these statistical methods in your everyday life?
**17. Statistical Literacy** Under what conditions is it appropriate to use a normal distribution to approximate the \(\hat{p}\) distribution?
**18. Statistical Literacy** What is the formula for the standard error of the normal approximation to the \(\hat{p}\) distribution? What is the mean of the \(\hat{p}\) distribution?
**19. Statistical Literacy** Is \(\hat{p}\) an unbiased estimator for \(p\) when \(np > 5\) and \(nq > 5\)? Recall that a statistic is an unbiased estimator of the corresponding parameter if the mean of the sampling distribution equals the parameter in question.
**20. Basic Computation: \(\hat{p}\) Distribution** Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose \( n = 33 \) and \( p = 0.21 \). Can](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff59662fb-eaec-4b3d-a1b9-c848915bfa7b%2Fda9538de-c346-40a8-8891-d6d9a73dbaaa%2Fsgg2uup_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**15.** The airline knows from past experience that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation will show up for the flight?
(b) Let \( n = 267 \) represent the number of ticket reservations. Let \( r \) represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation?
\[ P(255 \leq r); \, P(r \leq 255); \, P(r \leq 267); \, P(r = 255) \]
(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation?
**16. General: Approximations** We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which you discuss and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions made for each approximation. Give details and examples in your essay. How could you apply these statistical methods in your everyday life?
**17. Statistical Literacy** Under what conditions is it appropriate to use a normal distribution to approximate the \(\hat{p}\) distribution?
**18. Statistical Literacy** What is the formula for the standard error of the normal approximation to the \(\hat{p}\) distribution? What is the mean of the \(\hat{p}\) distribution?
**19. Statistical Literacy** Is \(\hat{p}\) an unbiased estimator for \(p\) when \(np > 5\) and \(nq > 5\)? Recall that a statistic is an unbiased estimator of the corresponding parameter if the mean of the sampling distribution equals the parameter in question.
**20. Basic Computation: \(\hat{p}\) Distribution** Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose \( n = 33 \) and \( p = 0.21 \). Can
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Step 1
From the given information,
Consider, X is the binomial distribution that is,
Probability of success = p
Sample size =n
Thus,
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