1. Describing the Sampling Distribution of X. A manufacturer of automobile batteries claims that the length of life for their batteries is normally distributed with a mean of 72 months and a standard deviation of 12 months (i.e. battery life N (72, 12)).

(a) Describe the sampling distribution of the sample mean for samples of size 16, i.e. describe the distribution of the average life time of these automobile batteries for samples of size 16.

i. Shape (Choose one): Normal Approximately Normal Not Normal

ii. Mean: (Do NOT round answer.)

iii. Standard Error: (Do NOT round answer.)

(b) How would your answer in part (a) change if the battery life follows a skewed right distribution?

i. Shape (Choose one): Normal Approximately Normal Not Normal

ii. Mean: (Do NOT round answer.)

iii. Standard Error: (Do NOT round answer.)

(c) How would your answer in part (a) change if the battery life follows a skewed right distribution and the sample size was 144 instead of 16?

i. Shape (Choose one): Normal Approximately Normal Not Normal

ii. Mean: (Do NOT round answer.)

iii. Standard Error: (Do NOT round answer.)