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 that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will last more than 5.25 minutes? Round to the nearest thousandth.
A)0.325
B)0.488
C)0.012
D)0.175

Question

Quizplus · Accepted Answer

To find the probability that the average song length will last more than 5.25 minutes, we use the Central Limit Theorem. The standard error (SE) is 1.10/sqrt(25) = 0.22. The z-score is (5.25 - 4.75) / 0.22 = 2.27. Using a standard normal distribution table, the probability of a z-score greater than 2.27 is approximately 0.012.

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