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.

1. What is the standard error of the mean?

2. What percent of the sample means will be greater than 137 seconds?

3. What percent of the cuts will exceed 137 seconds.

Answer 1

Solution:

1. What is the standard error of the mean?

Answer:

The standard error is:

2. What percent of the sample means will be greater than 137 seconds?

Answer:

We required to find here:

  

Now using the standard normal table we have:

Therefore, 0.62 percent of the sample means will be greater than 137 seconds.

3. What percent of the cuts will exceed 137 seconds?

Answer:

We required to find here:

  

Now using the standard normal table we have:

Therefore, 40.13 percent of the cuts will be exceed 137 seconds.