Scenario 1: A survey was conducted to measure the height of US males. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with mean of 69.2 inches and a standard deviation of 2.9 inches. A study participant is randomly selected.
(a) Find the probability that his height is less than 66 inches.
(b) Find the probability that his height is between 66 and 72 inches.
(c) Find the probability that his height is more than 72 inches.
Scenario 2: The monthly utility bills in a certain city are normally distributed, with mean of $100 and a standard deviation of $12. A utility bill is randomly selected.
(a) Find the probability that the utility is less than $80.
(b) Find the probability that the utility is between $80 and $115.
(c) Find the probability that the utility is more than $115 inches.