The extract of a plant native to Taiwan has been tested as a possible treatment
ID: 2932197 • Letter: T
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 79 and standard deviation of 8.9 grams per mililiter.
(a) What is the probability that the amount of collagen is greater than 69 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 2 standard deviations of the mean?
answer
Explanation / Answer
a) probability that the amount of collagen is greater than 69 grams per mililiter=P(X>69)
=P(Z>(69-79)/8.9)=P(Z>-1.1236)=1-P(Z<-1.1236)=1-0.1306 =0.8694
b) probability that the amount of collagen is less than 78 grams per mililiter=P(X<78)
=P(Z<(78-79)/8.9)=P(Z<-0.1124)=0.4553
c) percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean=P(-2<Z<2) =0.97725-0.02275 =0.9545~ 95.45%
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