Question

The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 60 and standard deviation of 8.1 grams per mililiter. Round all answers to 4 decimal places.

(a) What is the probability that the amount of collagen is greater than 60 grams per mililiter? answer:

(b) What is the probability that the amount of collagen is less than 78 grams per mililiter? answer:

(c) What percentage of compounds formed from the extract of this plant fall within 3 standard deviations of the mean? answer:

Answer 1

Solution:

Let X be a random variable which represents the amount of collagen obtain from a chemical compound produced from a plant native to Taiwan.

Given that, X ~ N(60, 8.1²)

i.e.  μ = 60 grams/ml and   σ = 8.1 grams/ml

a) We have to obtain P(X > 60 ).

We know that, if X ~ N(μ, σ^{​​​​​​2}) then

Using "NORM.S.DIST" function of excel we get,

P(Z > 0) = 0.5000

The probability that the amount of collagen is greater than 60 grams per milliliter is 0.5000.

b) We have to obtain P(X < 78).

We know that, if X ~ N(μ, σ^{​​​​​​2}) then

Using "NORM.S.DIST" function of excel we get,

P(Z < 2.2222) = 0.9869

The probability that the amount of collagen is less than 78 grams per milliliter is 0.9869.

c) According to empirical rule of normal distribution, about 99.73% of the observations fall within 3 standard deviations of the mean.

Hence, 99.73 percent of compounds formed from the extract of this plant fall within 3 standard deviations of the mean.

Please rate the answer. Thank you.