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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

In the following problems, use a normal approximation to the binomial.

Sales A smoking cessation program advertises that 60 % of all participants in its program quit smoking for at least 6 months. Suppose Consumer Checkup surveyed 400 “graduates” of the program and found that 220 had not smoked for 6 months following the end of the program. What is the probability that this will happen if the advertising claim is true?

To determine

To calculate: The probability that 220 out of 400 graduates of the program have quit the smoking.

Explanation

Given Information:

A smoking cessation program advertise that the 60% of all the participates of its program quit smoking for at least six months. It is given that 220 out of 400 graduates of the program have quit the smoking.

Formula used:

For a binomial distribution,

Mean is μ=np and standard deviation is,

σ=npq

The zscore is,

z=xμσ

Where, q=1p.

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

Calculation:

Consider A smoking cessation program advertise that the 60% of all the participates of its program quit smoking for at least six months.

So, the probability of number of participants quit the smoking is,

p=60%=60100=0.6

Then the mean is,

μ=np=400(0.6)=240

And the probability of failure is q=1p.

q=10.6=0.4

And the standard deviation is,

σ=npq=400(0.6)(0.4)=96=9

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