In a study of African American and Caucasian girls of ages 9 and 10 years, the girls recorded their diets in a diary for three days. The researcher then computed the daily salt intake. The distribution of daily salt intakes for the African American girls has a mean of 3073 mg and a standard deviation of 1072 mg. The distribution of daily salt intakes for the Caucasian girls has a mean of 2803 mg and a standard deviation of 833 mg. Assume the distributions of daily salt intakes for the African American girls and for the Caucasian girls are approximately normal.
a. Find the probability that a girl randomly selected from the African American girls had a daily salt intake of at most 1500 mg.
b. Find the probability that a girl randomly selected from the Caucasian girls had a daily salt intake of at most 1500 mg.
c. Explain how it is possible for the result you found in part (a) to be greater than the result you found in part (b), even though the mean intake of salt per day was larger for the African American girls than the Caucasian girls.