Answer to Question #325579 in MatLAB for Sonu

Question

11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.

For each of the following questions, construct a normal distribution curve and provide the answer.

a)    About what percent of the products last between 87 and 93 days?

b)    About what percent of the products last 84 or less days?

For each of the following questions, use the standard normal table and provide the answer.

c) About what percent of the products last between 89 and 94 days?

d) About what percent of the products last 95 or more days? 

Answer 1

a)That percentage of the product lies in the range of plus/minus standard deviation from the mean value, therefore it is equal to 68%

b) That are the products below two sigmas of mean value, the percentage of those products is 2.3%

c) 89 days corresponds to z = (89-90)/3 = -0.33, 94 days corresponds to z = (94-90)/3 = 1.33, therfore

$p = \Phi(1.33) - \Phi(-0.33) = 0.90824 - 0.37070 = 0.53754$ or 53.8%

d) 95 days corresponds to z = (95-90)/3 = 1.66, therefore $p = 1-\Phi(1.66) = 1 - 0.95154=0.04846$ or 4.8%