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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
3. In Pant Science (May 2010), a group of Japanese environmental scientists investigated the
ability of a hybrid tomato plant to produce miraculin. (Miraculin is a protein naturally produced in
a rare tropical fruit that can convert a sour taste into a sweet taste).For a particular generation of
the tomato plant, the amount x of miraculin produced had a mean of 105.3 and a standard
deviation of 8.0. Assume that x is normally distributed.
a) Find P(x >120)
b) Find P(100<x < 110)
c) Find the value a for which P(x < a)25
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3. In Pant Science (May 2010), a group of Japanese environmental scientists investigated the ability of a hybrid tomato plant to produce miraculin. (Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste).For a particular generation of the tomato plant, the amount x of miraculin produced had a mean of 105.3 and a standard deviation of 8.0. Assume that x is normally distributed. a) Find P(x >120) b) Find P(100<x < 110) c) Find the value a for which P(x < a)25

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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:

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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:

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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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