   Chapter 8.5, Problem 7E ### 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 5-18, find the normal approximation of the probability of96 successes in 180 trials if p = 0.4.

To determine

To calculate: The normal approximation of the probability for the provided binomial experiment, 96 successes in 180 trials if p=0.4.

Explanation

Given Information:

For 96 successes in n=180 and p=Pr(success)=0.4.

Formula used:

For a binomial distribution if, np5 and nq5 then the binomial distribution can be approximated accurately, with mean μ=np and standard deviation σ=npq.

Where n the number of trials, p is the probability of success, and q is the probability of failure q=1p.

And to convert the x values of binomial distribution in use z score use, z=xμσ,

The continuity correction to convert the binomial range of values to the corresponding interval of normal distribution values for any integer x is [x0.5,x+0.5].

Calculation:

Consider the binomial distribution n=180 and p=Pr(success)=0.4 then the mean of the binomial distribution is,

μ=npμ=180(0.4)μ=72

And the probability of failure is q=1p,

q=10.4q=0.6

And the standard deviation is,

σ=npqσ=180(0.4)(0.6)σ=43

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