Tomato as a taste modifier. Miraculin-a protein naturally produced in a rare tro

Question

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 r is normally distributed. Find P(x > 120). Find P(100

Explanation / Answer

We are given that the random variable x follows a normal distribution.

Mean = 105.3

SD = 8

Part a

We have to find P(X>120)

P(X>120) = 1 – P(X<120)

Z = (X – mean) / SD

Z = (120 – 105.3) / 8 = 1.8375

P(X<120) = P(Z<1.8375) = 0.966932

P(X>120) = 1 – P(X<120) = 1 - 0.966932 = 0.033068

Required probability = 0.033068

Part b

Here, we have to find P(100<X<110)

P(100<X<110) = P(X<110) – P(X<100)

First we have to find P(X<110)

Z = (110 – 105.3)/8 = 0.5875

P(X<110) = P(Z<0.5875) = 0.721566

Now, we have to find P(X<100)

Z = (100 – 105.3)/8 = -0.6625

P(X<100) = P(Z< -0.6625) = 0.253825

P(100<X<110) = P(X<110) – P(X<100) = 0.721566 - 0.253825 = 0.467741

Required probability = 0.467741

Part c

P(X<a) = 0.25

Z = (X – mean) / SD

X = Mean + Z*SD

Z = -0.67449

(By using normal table)

X = 105.3 – 0.67449*8 = 99.90408

Required answer: 99.90408

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---