**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 $."

Answered: The sample size n, probability of…

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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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= 0.78 q = 0.22 Can the normal distribution be used to approximate the random variable x? A. No, because nq < 5. B. Yes, because np 25 and nq 2 5. C. No, because np < 5 and nq < 5. D. No, because np < 5.
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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. n= 20 p= 0.38 q= 0.62 Can the normal distribution be used to approximate the random variable x? O A. No, because nq < 5. O B. No, because np <5 and nq < 5, OC. No, because np <5. OD. Yes, because np 25 and nq 2 5.
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