   Chapter 8.5, Problem 6E ### 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 of740 successes in 900 trials if p = 0.8.

To determine

To calculate: The normal approximation of the probability for the provided binomial experiment, 740 successes in 900 trials if p=0.8.

Explanation

Given Information:

For 740 successes in 900 trials if p=0.8.

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.

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 provided binomial distribution n=900 and p=Pr(success)=0.8 then the mean of the binomial distribution is,

μ=npμ=900(0.8)μ=720

And the probability of failure is q=1p.

q=10.8q=0.2

And the standard deviation is,

σ=npqσ=900(0.8)(0.2)σ=144σ=12

To find the probability that x is in the continuous interval from 7400.5=739

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