   Chapter 8, Problem 34RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For the binomial experiments in Problems 34-37, Find the normal approximation for the probability of50 successes in 200 trials when p =   0.2 .

To determine

To calculate: The normal approximation of the probability for 50 successes in n=200 and p=Pr(success)=0.2 for the binomial experiment.

Explanation

Formula used:

For a binomial distribution:

Mean is μ=np and standard deviation is σ=npq

And z score is, z=xμσ

q=1p

Where n the number of trials, p is the probability of success, and q is the probability of failure.

Calculation:

Consider the binomial distribution n=200 and p=Pr(success)=0.2 then the mean of the binomial distribution is,

μ=npμ=200(0.2)μ=40

And the probability of failure is q=1p

q=10.2q=0.8

And the standard deviation is,

σ=npqσ=200(0.2)(0.8)σ=32σ=5.66

We find the probability that x is in the continuous interval from 500

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