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; thus, it 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) b. Find P(100 < x < 110) c. Find the value a for which P(x < a) = .25

Answer 1

Answer:

a) .033  b) .4678 c) 100

Step-by-step explanation:

Distribution of miraculin produced is normal. To answer question we need to find the z-score of 100g, 110g and 120g miraculin

General formula for z score is given by

z=$\frac{X-M}{s}$ where

• X is the miraculin produced (120,110,100)
• M is the mean miraculin produced for a partucilar tomato plant, which is 105.3
• s is the standard deviation of the sample, which is 8.0

a)

z-score for 120 g miraculin is $\frac{120-105.3}{8}$ =1.8375 then

P(x > 120) = P(z>1.8375) = 0.033

b)

z-score for 110 g miraculin is $\frac{110-105.3}{8}$ = 0.5875

  z-score for 100 g miraculin is $\frac{100-105.3}{8}$ = -0,6625

P(100 < x < 110) = P(x>100) - P(x>110) =0.7462 - 0,2784 = 0.4678

c)

if P(x < a) = 0.25 then corresponding z score for a is -0.6745. From the above formula we can calculate a:

$\frac{a-105.3}{8}$ =-0.6625 which gives a= 100