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) for a sufficiently large sample size, such as 30. Therefore, all statements are true.

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