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

The Central Limit Theorem allows us to use the normal distribution to approximate the sampling distribution of the sample mean for a large enough sample size. Here, the sample size is 25, which is sufficient. The standard error is 1.10/sqrt(25) = 0.22. The z-score for 5.25 is (5.25 - 4.75) / 0.22 = 2.27. Using the standard normal distribution table, the probability of a z-score greater than 2.27 is approximately 0.012.

Suppose That the Average Country Song Length in America Is