The extract of a plant native to Taiwan has been tested as a possible treatment

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 73 and standard deviation of 5.8grams per mililiter.

(a) What is the probability that the amount of collagen is greater than 64 grams per mililiter?

answer:

(b) What is the probability that the amount of collagen is less than 73 grams per mililiter?

answer:

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

answer: %

Explanation / Answer

mean is 73 and s is 5.8

a) P(x>64)=P(z>(64-73)/5.8)=P(z>-1.55) =P(z<1.55) =0.9394 , from normal distribution table

b) P(x<73)=P(z<0)=0.5

c) 99.7% fall within 3 standard deviations using empirical rule

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