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Question 9: Use R to answer the following. Let X have a binomial distribution with parameters n=25 and p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation (with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation. (a) P(15 ≤X ≤ 20) (b) P(X ≤ 15) (c) P(20 < X)

Question 9: Use R to answer the following. Let X have a binomial distribution with parameters n=25 and p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation (with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation. (a) P(15 ≤X ≤ 20) (b) P(X ≤ 15) (c) P(20 < X)

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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Question 9: Use R to answer the following. Let X have a binomial distribution with parameters n = 25 and p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation (with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation. (a) P(15 ≤X ≤ 20) (b) P(X ≤ 15) (c) P(20 < X)
Transcribed Image Text:Question 9: Use R to answer the following. Let X have a binomial distribution with parameters n = 25 and p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation (with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation. (a) P(15 ≤X ≤ 20) (b) P(X ≤ 15) (c) P(20 < X)
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Step 1

Solution -given that. n=25  p=0.60 then by using r software to solve the following problem

a) P(15≤X≤20)=?

> n<-25
> p<-0.6
> n*p
[1] 15
> n*(1-p)
[1] 10
> mean<-n*p
> SD<-sqrt(n*p*(1-p))
> # To find P(15<=X<=20) by using below code
> pnorm(20.5,mean,SD)-pnorm(14.5,mean,SD)    #(a)
[1] 0.5684994

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