39 Most powerful American women. Fortune (Oct. 16, 2008)

published a list of the 50 most powerful women in America.

The data on age (in years) of each woman is stored in the WPOWER50 file. The ages in the data set can be shown to be approximately normally distributed with a mean of 50 years and a standard deviation of 6.4 years. A powerful woman is randomly selected from the data, and her age is observed.

a. Find the probability that her age will fall between 55 and 60 years.

b. Find the probability that her age will fall between 48 and 52 years.

c. Find the probability that her age will be less than 35 years.

d. Find the probability that her age will exceed 40 years.

e. A 25-year-old woman claims she is one of the 50 most powerful women. Do you believe her? Explain.