Question

Lucille has a collection of more than 500 songs on her phone that have a mean duration of 215 seconds

and a standard deviation of 35 seconds. Suppose that every week she makes a playlist by taking an SRS of
49 of these songs, and we calculate the sample mean duration of the songs in each sample.

Answer 1

mean: 215

Standard deviation: 5

Explanation:

Khan Academy.

Answer 2

5

Explanation:

The sample mean is given by dividing the standard deviation by the squareroot of SRS

Given standard deviation of 35 and SRS of 49, we know that the squareroot of 49 is 7 ie √49=7

By substituting the given values we can obtain the sample mean as follows.

sample mean=35/√49=35/7=5

The sample mean for the given question is hence 5