Assume that male and female heights are both normally distributed with a male average of 69.1 inches with standard deviation of 2.8 inches, and a female average of 64.0 inches with standard deviation 2.5 inches. If a male and female go out on a date, what is the probability that the female is taller than the male? Show work.

Suppose that heights of women at UT Tyler are normally distributed with a mean of 64 inches and a standard deviation of 2.4 inches.    Find the probability that a collection of 16 women have an average height less than 62 inches tall.

A report claimed that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assuming the variable is normally distributed and the standard deviation is 3 hours. If 40 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours.

When Freshman 15 The term "Freshman 15" refers to the claim that college students typically gain 15 lb during their freshman year at college. Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 2.6 lb and a standard deviation of 10.8 1b (based on Data Set 13 "Freshman 15"). Find the probability that a randomly selected male college student gains 15 lb or more during his freshman year. What does the result suggest about the claim of the "Freshman 15"?