Question

CRA CDs, Inc. wants the mean lengths of the “cuts” on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a standard deviation of 8 seconds. Suppose we select a sample of 100 cuts from various CDs sold by CRA CDs, Inc. What can we say about the shape of the distribution of the sample means and why can we say this in (a)?

Answer 1

Ans: We know that when the sample size is equal to 30 or more than 30 and the standard deviation of the population is finite. Then, the distribution of the sample mean follows a normal distribution (approximately) by Central Limit Theorem. Therefore, we can say about the shape of the distribution of the sample means is that symmetric. Further, the mean and standard error of the sample mean are mean of the variable and standard deviation of the variable divided by square root of sample size. Therefore,

I can't find (a). So, I can't give any further comment.