Problem

Use the results from a survey of a simple random sample of 1099 adults. Among the 1099 respondents, $87 \%$ rated themselves as above average drivers We want to test the claim that more than $\frac{3}{4}$ of adults rate themselves as above average drivers. Complete parts (a) through (e). a. Regardless of the conclusion reached from the hypothesis test, is it possible that more than $\frac{3}{4}$ of adults can be above average drivers? A. Yes. Assuming quality of driving can be quantified, a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean. B. Yes. Assuming quality of driving can be quantified, a distribution that is extremely skewed to the right would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean. C. No. Assuming quality of driving can be quantified, half of all adults must have driving quality less than or equal to the mean. D. No. It is impossible to compare the quality ofldifferent adults' driving.

Solution

Step 1 :The question is asking whether it's possible for more than 75% of adults to be above average drivers. This is a theoretical question about the nature of averages and distributions, rather than a computational problem.

Step 2 :The average (or mean) of a distribution is calculated by summing all the values and dividing by the number of values. In a perfectly symmetrical distribution, half the values will be above the mean and half will be below. However, in a skewed distribution, it's possible for more than half the values to be above or below the mean.

Step 3 :In this case, we're considering whether more than 75% of adults could be above average drivers. This would require a distribution that is heavily skewed to the left, with a large number of adults having a driving quality just above the mean and a smaller number having a driving quality significantly below the mean.

Step 4 :Therefore, the correct answer is A: Yes. Assuming quality of driving can be quantified, a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean.

Step 5 :\(\boxed{\text{A. Yes. Assuming quality of driving can be quantified, a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean.}}\)

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Source: https://solvelyapp.com/problems/18583/

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