Suppose that X is a binomial random variable with n =200

Chapter 4, Problem 95E

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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)

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

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