..ooo AT&T; Wi-Fi 2796 4:28 PM math.csi.cuny.edu (1 pt) The extract of a plant n

Question

..ooo AT&T; Wi-Fi 2796 4:28 PM math.csi.cuny.edu (1 pt) 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 62 and standard deviation of 8 grams per mililiter. (a) What is the probability that the amount of collagen is greater than 61 grams per mililiter? answer: 0.5497 (b) What is the probability that the amount of collagen is less than 86 grams per mililiter? answer: 0.9987 (c) What percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean? answer.

Explanation / Answer

Solution:

z = (X-Mean)/S.D
a) z value corresponding to X=61 is
z = (61-62)/8 = - 0.125
Required probability = Area under the standard normal curve right to z = - 0.125
= 0.5497

b) z value corresponding to X=86 is
z = (86-62)/8= 3
Required probability = Area under the standard normal curve left to z = +3
= 0.9987

c) % of compounds formed from the extract of this plant fall within 2 standard deviations of the mean

= 95.45 %

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