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 6868 and standard deviation of 9.3 grams per mililiter. Round all answers to 4 decimal places.

(a)  What is the probability that the amount of collagen is greater than 6666 grams per mililiter?

answer:

(b)  What is the probability that the amount of collagen is less than 8282 grams per mililiter?

answer:

(c)  What percentage of compounds formed from the extract of this plant fall within 11 standard deviations of the mean?

answer:  %

Answer 1

µ = 68

sd = 9.3

a)

                            

                             = P(Z > -0.43)

                             = 1 - P(Z < -0.43)

                             = 1 - 0.3336

                             = 0.6664

b)

                             

                              = P(Z < 1.51)

                              = 0.9345

c) P(within 1 standard deviations) = P(-1 < Z < 1)

                                                      = P(Z < 1) - P(Z < -1)

                                                      = 0.8413 - 0.1587

                                                      = 0.6826

                                                      = 68.26%