Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40- 44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.
-Suppose the process of taking random samples of size 30 from the 40- 44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?
A)The histogram will be roughly bell- shaped.
B)The histogram will be unimodal.
C)The histogram will be roughly symmetrical.
D)All of these statements are true.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal (bell-shaped and symmetrical) if the sample size is large enough, regardless of the population distribution. Since the sample size is 30, the histogram of the sample means will be roughly bell-shaped, unimodal, and symmetrical.

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