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) P(100 < x < 110) c) Find the value a for which P(x < a) = .25

a) P(x > 120) = 0.03288

b) P(100 < x < 110) = 0.46777

c) value of a for which P(x < a) = 0.25

a = 99.91

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 105.3

Standard deviation = σ = 8.0

a) P(x > 120)

To work this, we first need To convert 120 go standardized/normalized/z-scores.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (120 - 105.3)/8.0 = 1.84

To determine P(x > 120) = P(z > 1.84)

We use the tables for these probabilities now.

P(x > 120) = P(z > 1.84) = 1 - P(z ≤ 1.84) = 1 - 0.96712 = 0.03288

b) P(100 < x < 110)

We normalize the two value in the inequality

For 100,

z = (x - μ)/σ = (100 - 105.3)/8.0 = -0.66

For 110,

z = (x - μ)/σ = (110 - 105.3)/8.0 = 0.59

To determine P(100 < x < 110) = P(-0.66 < z < 0.59)

We use the tables for these probabilities now.

P(100 < x < 110) = P(-0.66 < z < 0.59) = P(z < 0.59) - P(z < -0.66) = 0.72240 - 0.25463 = 0.46777

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

Let the z-score of a be z'

z' = (x - μ)/σ = (a - 105.3)/8.0

P(x < a) = P(z < z') = 0.25

Using the table, z' = - 0.674

-0.674 = (a - 105.3)/8

a - 105.3 = -5.392

a = 105.3 - 5.392 = 99.91

Hope this Helps!!!

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq