Question

The most recent public health statistics available indicate that 23.6​% of American adults smoke cigarettes. Using the​ 68-95-99.7 Rule, describe the sampling distribution model for the proportion of smokers among a randomly selected group of 40 adults. Be sure to discuss your assumptions and conditions.

Describe the sampling distribution.

There is a​ 68% chance that between (answer-percent) and (answer-percent) are​ smokers, a​ 95% chance that between (answer-percent) and (answer-percent) are​ smokers, and a​ 99.7% chance that between (answer-percent) and (answer-percent) are smokers.

​(Round to one decimal place as​ needed.)

Answer 1

Given that 23.6% american adults do smoke

Hence Mean proportion = 0.23

Standard deviation(SD) =

SD =

SD = 0.067

Hence the Standard deviation of proportion = 6.7%

We have information that 68% data falls in between 1 SD of mean

That is = [23.6 +or- 6.7]

Hence we have [16.9%, 30.3%]
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Given 95% data in 2 SD mean

Then repeat the same with

[23.6 +or- (2*6.7)]

[10.2%. 37%]

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Given 99.7% falls between 3 SD of mean

Hence [23.6 +or- (3*6.7)]

[3.5%, 43.7%]

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Thanks