Solution Found!
Suppose that X is a binomial random variable with n =200
Chapter 4, Problem 95E(choose chapter or problem)
Suppose that X is a binomial random variable with n = 200 and p = 0.4. Approximate the following probabilities:
(a) \(P(X \leq 70)\) (b) \(P(70<X<90)\) (c) \(P(X=80)\)
Equation transcription:
Text transcription:
P(X \leq 70)
P(70<X<90)
P(X=80)
Questions & Answers
QUESTION:
Suppose that X is a binomial random variable with n = 200 and p = 0.4. Approximate the following probabilities:
(a) \(P(X \leq 70)\) (b) \(P(70<X<90)\) (c) \(P(X=80)\)
Equation transcription:
Text transcription:
P(X \leq 70)
P(70<X<90)
P(X=80)
ANSWER:Step 1 of 4
Given that X is a binomial random variable with n=200 and p=0.4
The approximation is good for
Here np=200(0.4)=80
And nq=200(1-0.4)=120
To approximate a binomial probability with normal distribution ,a continuity correction will apply that is
And
Now mean () = np
= 80
And standard deviation ()=
=
= 6.93