A rental car company has noticed that the distribution of the number of miles customers put on rental cars per day is somewhat skewed to the right, with an occasional high outlier. The distribution has a mean of 80 miles and a standard deviation of 50 miles.
a. Draw a picture of a normal curve with this mean and standard deviation (80 miles and 50 miles), and use the information in the picture to verify that the distribution of number of miles must be skewed to the right and/or have occasional high outliers rather than being normally distributed.
b. What is the approximate distribution for the mean number of miles per day put on a typical one of the company's rental cars in a year (365 days)?
c. What is the approximate distribution for the total number of miles put on a typical one of the rental cars in a year (365 days)?
d. Do you think the necessary conditions for the approximate normality of the sampling distribution in part (b) are met in this situation? Explain.