Question

Suppose a carnival director in a certain city imposes a height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.5 feet and a standard deviation of 0.8 feet (patrons are mostly children). Make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, and state your found value from Table A4.

a) What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain?

b) A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet?

c) Another group of 5 friends wants to ride Terror Mountain. What is the probability that their mean height is between 4 and 4.25 feet, inclusive?

Answer 1