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 72 and a standard deviation of 7.2 grams per milliliter.

(a)  What is the probability that the amount of collagen is greater than 61 grams per milliliter?

answer:

(b)  What is the probability that the amount of collagen is less than 88 grams per milliliter?

answer:

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

answer:  %

Answer 1

Solution :

Given ,

mean = = 72

standard deviation = =7.2

P(x >61 ) = 1 - P(x<61 )

= 1 - P[(x -) / < (61-72) /7.2 ]

= 1 - P(z <-1.53 )

Using z table

= 1 - 0.0630

=0.9370

probability=0.9370

(b)

P(X< 88) = P[(X- ) / < (88-72) /7.2 ]

= P(z < 2.22)

Using z table

= 0.9868

probability=0.9868

(c)using empirical rule

within 3 standard deviations of the mean = 99.7%