Davids iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviution of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time $\bar{x}$ of these songs. What are the mean and the standard deviation of the sampling distribution of $\bar{x}$ ? Explain.
Added by Joseph R.
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The mean of the sampling distribution of $\bar{x}$ is equal to the mean of the population. So, the mean of the sampling distribution is 225 seconds. Show more…
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Songs on an iPod David's iPod has about $10,000$ songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of $60 \mathrm{seconds}$. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time $\overline{x}$ of these songs. What are the mean and the standard deviation of the sampling distribution of $\overline{x} ?$ Explain.
Meher G.
David's iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Describe the shape of the sampling distribution of x̄ for SRSs of size n=5 from the population of songs on David's iPod. Justify your answer.
Thuc N.
Songs on an iPod Refer to Exercise 49. (a) Explain why you cannot safely calculate the probability that the mean play time $\overline{x}$ is more than 4 minutes $(240 \text { seconds) for an } \mathrm{SRS} \text { of } 10 \text { songs. }$ (b) Suppose we take an SRS of 36 songs instead. Explain how the central limit theorem allows us to find the probability that the mean play time is more than 240 seconds. Then calculate this probability. Show your work.
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