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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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 of

more than 120 successes in 200 trials if p = 0.6.

To determine

To calculate: The normal approximation of the probability for the provided binomial experiment, more than 120 successes in 200 trials and p=0.6.

Explanation

Given Information:

More than 120 successes in n=200 and p=Pr(success)=0.6.

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=200 and p=Pr(success)=0.6 then the mean of the binomial distribution is,

μ=npμ=200(0.6)μ=120

And the probability of failure is q=1p,

q=10.6q=0.4

And the standard deviation is,

σ=npqσ=200(0

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