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

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 8.3 grams per mililiter.

(a) What is the probability that the amount of collagen is greater than 68 grams per mililiter?

(b) What is the probability that the amount of collagen is less than 72 grams per mililiter?

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

Solution

x= amount of collagen
a)p( x > 68 ) = p ( z > (68 - 73 ) / 8.3 ) = 1 - p ( z <= - 0.602409638) =  0.7265493......

b) p ( x < 72 ) = p ( z < (72 - 73) / 8.3 ) = p ( z < -0.1204819 ) = 0.4520507.......

c) mean + 3* s.d = 97.9.......mean - 3* s.d = 48.1.......

p( 48.1 < x < 97.9 ) = p ( x < 97.9 ) - p ( x < 48.1 ) = p ( z < 3 ) - p ( z < -3 )
= 0.9986501 - 0.001349898 = 0.9973002