The length of the thorax in a population of male fruit flies

The length of the thorax in a population of male fruit flies is approximately Normal with mean 0.810 millimeters (mm) and standard deviation 0.084 mm. Use the 68-95-99.7 rule to answer the following questions. Hint: Page 159 in Text.

(a) What range of lengths covers almost all (99.7%) of this distribution? (Round your answers to three decimal places.)
between BLANK and BLANK mm

(b) What percent of male fruit flies have a thorax length exceeding 0.894 mm?

________ %

Solution

a)
P ( Z < x ) = 0.997
Value of z to the cumulative probability of 0.997 from normal table is 2.748
P( x-u/s.d < x - 0.81/0.084 ) = 0.997
That is, ( x - 0.81/0.084 ) = 2.75
--> x = 2.75 * 0.084 + 0.81 = 1.0408                  
b)
P(X > 0.894) = (0.894-0.81)/0.084
= 0.084/0.084 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587