Question

A rental car company has noticed that the distribution of the number of miles customers put on rental cars per day is skewed to the right, with some occasional high outliers. The distribution has a mean of 80 miles and a standard deviation of 50 miles.
Which of the following distributions would have the smallest standard deviation?

(a) Number of miles put on a rental car in one day
(b) Average number of miles put on a rental car per day across 5 customers
(c) Average number of miles put on a rental car per day across 25 customers
or (d) Distributions of all of the above would have the same standard deviation.

Answer 1

Using the Central Limit Theorem, the correct option is:

(c) Average number of miles put on a rental car per day across 25 customers.

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The Central Limit Theorem states that, for a normally distributed variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means of size m are approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

• The interpretation related to this problem is that the larger the sample size, the smaller the standard deviation.
• Thus, among the options, the largest sample is 25, thus, option c will have the smallest standard deviation.

A similar problem is given at brainly.com/question/23088374