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 71 and a standard deviation of 9.4 grams per milliliter.

(a) What is the probability that the amount of collagen is greater than 62 grams per milliliter?
(b) What is the probability that the amount of collagen is less than 74 grams per milliliter?

The normal distribution also known as the bell curve is a probability function that explains natural random events in almost every field of human knowledge.

The function to compute the probability of a range of values of the independent variable depends on two values: The mean [tex]\mu[/tex] and the standard deviation [tex]\sigma[/tex]. It's not possible to use a direct formula to know the cumulative probability, usually the left tail of the bell curve. We must use some sort of table or digital means to take such values. We use the Excel Normal Distribution formula:

NORM.DIST(x,mean,standard_dev,cumulative)

The question provides the two needed parameters: [tex]\mu=71,\ \sigma=9.4[/tex]. We'll now compute the required probabilities:

(a) P(x>62). Since the table gives us the left tail of the curve and we want to compute the right tail, we simply subtract the result from 1. That is

[tex]P(x>62)=1-P(x<62)[/tex]

We now use the Excel formula:

NORM.DIST(62,71,9.4,true)=0.1692

[tex]P(x>62)=1-P(x<62)=1-0.1692=0.8308[/tex]

(b) P(x<74)=NORM.DIST(74,71,9.4,true)=0.6252

[tex]P(x<74)=0.6252[/tex]