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The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable x. q=0.25 n = 19 0000 Can the normal distribution be used to approximate the random variable x? A. No, because nq < 5. B. No, because np <5 and nq < 5. p=0.75 OC. No, because np < 5. O D. Yes, because np 25 and nq 25. www.

The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable x. q=0.25 n = 19 0000 Can the normal distribution be used to approximate the random variable x? A. No, because nq < 5. B. No, because np <5 and nq < 5. p=0.75 OC. No, because np < 5. O D. Yes, because np 25 and nq 25. www.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem Statement:** The sample size \( n \), probability of success \( p \), and probability of failure \( q \) are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable \( x \). - \( n = 19 \) - \( p = 0.75 \) - \( q = 0.25 \) --- **Question:** Can the normal distribution be used to approximate the random variable \( x \)? - A. No, because \( nq < 5 \). - B. No, because \( np < 5 \) and \( nq < 5 \). - C. No, because \( np < 5 \). - D. Yes, because \( np \geq 5 \) and \( nq \geq 5 \). --- **Explanation:** To determine whether the normal distribution can approximate a binomial distribution, the following conditions should be satisfied: 1. \( np \geq 5 \) 2. \( nq \geq 5 \) Where: - \( np \) is the expected number of successes. - \( nq \) is the expected number of failures. Based on the given values: - Calculate \( np = 19 \times 0.75 = 14.25 \) - Calculate \( nq = 19 \times 0.25 = 4.75 \) Therefore, \( np \geq 5 \) but \( nq < 5 \), so option A is correct: "No, because \( nq < 5 \)."
Transcribed Image Text:**Problem Statement:** The sample size \( n \), probability of success \( p \), and probability of failure \( q \) are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable \( x \). - \( n = 19 \) - \( p = 0.75 \) - \( q = 0.25 \) --- **Question:** Can the normal distribution be used to approximate the random variable \( x \)? - A. No, because \( nq < 5 \). - B. No, because \( np < 5 \) and \( nq < 5 \). - C. No, because \( np < 5 \). - D. Yes, because \( np \geq 5 \) and \( nq \geq 5 \). --- **Explanation:** To determine whether the normal distribution can approximate a binomial distribution, the following conditions should be satisfied: 1. \( np \geq 5 \) 2. \( nq \geq 5 \) Where: - \( np \) is the expected number of successes. - \( nq \) is the expected number of failures. Based on the given values: - Calculate \( np = 19 \times 0.75 = 14.25 \) - Calculate \( nq = 19 \times 0.25 = 4.75 \) Therefore, \( np \geq 5 \) but \( nq < 5 \), so option A is correct: "No, because \( nq < 5 \)."
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