Approximately Normal for Sample Mean

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.

• Because n = 5 ≥ 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 5 ≥ 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

• Because n = 5 < 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 5 < 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

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 = 100 from the population of songs on David's iPod. Justify your answer.

• Because n = 100 ≥ 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 100 ≥ 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

• Because n = 100 < 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 100 < 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is μ = $250 with a standard deviation of σ = $5000. The distribution of losses is strongly right-skewed: Many policies have $0 loss, but a few have large losses. Describe the shape of the sampling distribution of x̄ for SRSs of size n = 15 from the population of homeowners. Justify your answer.

• Because n = 15 ≥ 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 15 ≥ 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

• Because n = 15 < 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 15 < 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is μ = $250 with a standard deviation of σ = $5000. The distribution of losses is strongly right-skewed: Many policies have $0 loss, but a few have large losses. Describe the shape of the sampling distribution of x̄ for SRSs of size n = 1000 from the population of homeowners. Justify your answer.

• Because n = 1000 ≥ 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 1000 ≥ 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.

• Because n = 1000 < 30, the sampling distribution of x̄ is approximately normal by the central limit theorem.

• Because n = 1000 < 30, the sampling distribution of x̄ will also be skewed to the right, but not quite as strongly as the population.