According to the US Department of Agriculture, the annual amount of apples eaten by a randomly chosen woman is normally distributed with a mean of 19.8 pounds and a standard deviation of 3.2 pounds.
(a) What percentage of women have an annual consumption of less than 15 pounds of apples?
(b) What percentage of women annually consume between 15 and 20 pounds of apples?
c) What annual apple weight separates the top 75% of adult women from the bottom 25%? What do we call this value?
(d) At what weight of apples would a randomly chosen woman consume more than 90% of all adult women? (i.e.: 90% of all annual apple consumption weights are less than what value?)
(e) Between what two weights do 80% of the weights in this distribution fall? [Note that there is not a unique answer to this question.]
(f) Now suppose the true standard deviation of annual apple consumption weights is unknown. If 70% of all weights were less than 22 pounds, what would the standard deviation of annual apple weights be?