Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical f...

Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science(May 2010) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise. Recall that the amount x of miraculin produced in the plant had a mean of 105.3 micro-grams per gram of fresh weight with a standard deviation of 8.0. Consider a random sample of n= 64 hybrid tomato plants and let   represent the sample mean amount of miraculin produced. Would you expect to observe a value of   less than 103 micrograms per gram of fresh weight? Explain.

Tomato as a taste modifier. Miraculin—a protein naturally produced in a rare tropical fruit—can convert a sour taste into a sweet taste. Consequently, miraculin 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.

a. Find P(x> 120).

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b. Find P(100<x< 110).

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c. Find the value a for which P(x < a) = .25.