Chapter 4.6, Problem 4.99ACB

Tomato as a taste modifier. Miraculin—a protein naturally produced in a rare tropical fruit—has the potential to be an alternative low-calorie sweetener. In Plant Science (May 2010), a group of Japanese environmental scientists investigated the ability of a hybrid tomato plant to produce miraculin. For a particular generation of the tomato plant, the amount x of miraculin produced (measured in micrograms per gram of fresh weight) had a mean of 105.3 and a standard deviation of 8.0. Assume that x is normally distributed.

1. a. Find P (x > 120).
2. b. Find P (100 < x < 110).
3. c. Find the value a for which P ( x < a) = .25.