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 0.760 millimeters (mm) and standard deviation 0.075 mm. Use the 68-95-99.7 rule to answer the following questions.

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

between _______and ________ mm  

(b) What percent of male fruit flies have a thorax length exceeding 0.835 mm?  

Solution

a)

99.7% is covered by numbers 3 standard deviations above or below the mean.

Thus,

lower bound = u - 3s = 0.760 - 3*0.075 = 0.535
upper bound = u + 3s = 0.760 + 3*0.075 = 0.985

Thus, between 0.535 and 0.985 mm [ANSWER]

***********************

b)

here, for 0.835,

z = (x-u)/s = (0.835-0.760)/0.075 = 1

Thus, it is 1 standard deviation above the mean.

Thus, those which exceed 0.835 mm is (1-0.68)/2 = 16% [ANSWER]