A survey of 48 randomly selected "iPhone" owners showed that the purchase price has a mean of $419 with a sample standard deviation of $180.

a. Compute the standard error of the sample mean. (Round the final answer to the nearest whole number.)

Standard error

b. Compute the 80% confidence interval for the mean. (Round the final answers to 2 decimal places.)

The confidence interval is between $ and $ .

c. How large a sample is needed to estimate the population mean within $14 at a 80% degree of confidence? (Round the final answer to the nearest whole number.)

Sample size