2. Data from the CDC states that the average time it takes a 13-year-old girl to run a mile is 11 minutes with a standard deviation of 2 minutes. The data follows a normal distribution.

a. Calculate the probability that a randomly selected individual 13-year-old girl could run a mile in 9.5 minutes or less. Would you be surprised if you selected one individual girl and her time to run a mile is 9.5 minutes? Why or why not? Draw and label a normal curve for this situation.

b. Suppose a random sample of 30 13-year-old girls is selected.

Calculate the probability that the sample average (x-bar) is 9.5 minutes or less. Would you be surprised if your sample average for this group of 30 girls is 9.5 minutes? Why or why not? Draw and label a normal curve for this situation.