Chapter 7.3, Problem 63E

(a)

To determine

To Explain: the shape of the sampling distribution of $\overline{x}$ for SRS of size n=5 from the population of songs on researcher’s iPod.

Answer to Problem 63E

Heavily skewed to the right

Explanation of Solution

The population distribution is heavily skewed to the right.

  $n=5$

Central limit theorem: if the sample size is large (30 or more), then the sampling distribution of the sample mean $\overline{x}$ is about normal.

Since the sample size of 5 is less than 30, it cannot be used the central limit theorem. In this case, the sampling distribution of the sample mean has the same shape as the population distribution and therefore the sampling distribution of the sample mean is heavily skewed to the right.

(b)

To determine

To Explain: the shape of the sampling distribution of $\overline{x}$ for SRSs of size n=100 from the population of songs on researcher’s ipod.

Answer to Problem 63E

Approximately normal

Explanation of Solution

The population distribution is heavily skewed to the right.

  $n=100$

Central limit theorem: if the sample size is large (30 or more), then the sampling distribution of the sample mean $\overline{x}$ is about normal.

Since the sample size of $100$ is more than $30$ , it can be used the central limit theorem and the sampling distribution of the sample mean is about Normal.