Suppose that the average pop song length in America is 4 minutes with a standard deviation of 1.25 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 be less than 3.5 minutes? Round to the nearest thousandth.
A)0.345
B)0.477
C)0.023
D)0.155

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n ≥ 30 is a common rule of thumb, but n = 25 is often sufficient). The standard error is 1.25/√25 = 0.25. The z-score for 3.5 is (3.5 - 4) / 0.25 = -2. The probability of a z-score being less than -2 is approximately 0.023.

Suppose That the Average Pop Song Length in America Is