1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ra1l [238]
3 years ago
11

Miraculin - a protein naturally produced in a rare tropical fruit - can convert a sour taste into a sweet taste. Consequently, m

iraculin 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 .
Mathematics
1 answer:
sineoko [7]3 years ago
8 0

Answer:

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 <em>Mean, </em>\mu<em> = 105.3  and  Standard Deviation, </em>\sigma<em> = 8.0</em>

Also, since x is normally distributed so;

                    Z = \frac{x - \mu}{\sigma} follows N(0,1)

a) P(x > 100) = P( \frac{x - \mu}{\sigma} > \frac{100 - 105.3}{8.0} ) = 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( \frac{x - \mu}{\sigma} < \frac{110 - 105.3}{8.0} ) = P(Z < 0.59) = 0.72240

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

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

                       ⇒ P( \frac{x - \mu}{\sigma} < \frac{a - 105.3}{8.0} ) = 0.25

                       ⇒ P(Z < \frac{a - 105.3}{8.0} ) = 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.

                     \frac{a - 105.3}{8.0} = 0.6745

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

You might be interested in
Simplify 2 (n+1) + n² + 4 (n-3)
Gala2k [10]
2 (n+1) + n² + 4 (n-3) 
= 2n + 2 +  n² + 4n - 12 ...expand by using distributive property
=  n² + 6n - 10 ...combine like terms

hope it helps
4 0
2 years ago
Read 2 more answers
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
Tema [17]
A is true--------------------------
6 0
3 years ago
Armando graphed the relationship between temperature and elevation for several cities. The
Novosadov [1.4K]

Answer:

,lokiu8ytfvgbhnjmkiom nb bnvmkjb nnjn7

Step-by-step explanation:

5 0
3 years ago
Who is correct between the two of them?
deff fn [24]

Answer:

Neither.

Step-by-step explanation:

I am not completely sure, so make sure to also let other answer this before you trust me lol. I really hope this helps!!

3 0
3 years ago
If the freshman class of 63 students has 11 more boys than girls, determine how many of each are in the class.g 1
torisob [31]
B + G = 63
B = G + 11

G + 11 + G = 63
2G + 11 = 63
2G = 63 - 11
2G = 52
G = 52/2
G = 26 <=== 26 girls

B = G + 11
B = 26 + 11
B = 37 <=== 37 boys

4 0
3 years ago
Other questions:
  • sharon has some almonds. after buying another 350 grams of almonds,she now has 1,230 grams of almonds. How many almond did Sharo
    8·1 answer
  • Let’s say a GWC coder is working on a project that includes 6 x (8 +7) lines of code. Rewrite this expression in words.
    14·1 answer
  • What is the value 1I 2L 3F 4
    13·2 answers
  • Brainilest!!! 50pts<br><br> Solve for x and y<br><br> 45x+(-326y)=96<br> 666x-777y=420
    7·2 answers
  • Number 15 really need help
    14·2 answers
  • Trey runs each lap in 6 minutes. He will run at least 30 minutes today. What are the possible numbers of laps he will run today?
    15·1 answer
  • Can somebody help me with this problem. And make sure that u can explain how to do it don't just give me the answer.
    6·1 answer
  • Crazy Valentine's day Work sheet. SOOOO CONFUSEDDD! Answered 1 and 3.
    6·1 answer
  • Can someone help me out? Will mark brainiest
    15·1 answer
  • To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $5.40 per hour. The chemistr
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!