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 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 .

a) P(x > 120) = 0.74537

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

c) Value of a = 110.7

Step-by-step explanation:

Let x = amount of miraculin produced (measured in micro grams per gram of fresh weight)

We are given Mean, = 105.3  and  Standard Deviation, = 8.0

Also, since x is normally distributed so;

                    Z = follows N(0,1)

a) P(x > 100) = P( > ) = P(Z > -0.6625) = P(Z < 0.66) = 0.74537

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

     P(x <= 100) = 1 - P(x > 100) = 1 - 0.74537 = 0.25463

     P(x < 110) = P( < ) = P(Z < 0.59) = 0.72240

Hence, P(100 < x < 110) = 0.72240 - 0.25463 = 0.46777

c) Given expression is P(x < a ) = 0.25

                       ⇒ P( < ) = 0.25

                       ⇒ P(Z < ) = 0.25

By seeing the Z % table we find that the value of z which have an are of 25% is 0.6745 i.e.

                      = 0.6745

So, value of a = 0.6745*8 + 105.3 = 110.7 .        

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude

if e is the midpoint of bd, then bd is 14.

step-by-step explanation: