# 3. In Pant Science (May 2010), a group of Japanese environmental scientists investigated theability of a hybrid tomato plant to produce miraculin. (Miraculin is a protein naturally produced ina rare tropical fruit that can convert a sour taste into a sweet taste).For a particular generation ofthe tomato plant, the amount x of miraculin produced had a mean of 105.3 and a standarddeviation of 8.0. Assume that x is normally distributed.a) Find P(x >120)b) Find P(100

Question
Step 1

Standard normal distribution:

The standard normal distribution is a special case of normal distribution. The standard normal distribution will have mean 0 and standard deviation 1. If a random variable y follows normal distribution with mean (m) and standard deviation (s), then the standard normal variable z will be as given below:

Step 2

a.

Find the probability of x > 120:

The random variable x (Amount of miraculin produced) follows normal distribution with mean 105.3 and standard deviation 8.0.

That is, E(x) = 105.3 and S.D(x) = 8.

The value of P(x > 120) is obtained as 0.03288 from the calculation given below:

Step 3

b.

Find the probability of 100 < x < 110:

The value of P(100 < x < 110) is obtained as 0.46777...

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