find 6 P79 36 Fruit flies The length of the thorax in a popu

6. P79 3.6 Fruit flies. The length of the thorax in a population of male fruit flies is approximate Normal with mean 0.8 millimeters (mm) and standard deviation 0.078mm. 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? b) What percent of male fruit flies have a thorax length exceeding 0.878mm?

Solution

a)

By empirical rule, you add/subtract 3 standard deviations from the mean to get the range.

Thus,

lower bound = 0.8 - 0.078*3 = 0.566
upper bound = 0.8 + 0.078*3 = 1.034

Thus, the range is from 0.566 to 1.034. [answer]

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

0.878 is 1 standard deviation away from 0.8 mm.

Thus, the numbers within one standard deviation is 68%.

Hence, 32% is out of this interval, for two tails.

As we only want those greater than 0.878, we only want one of those two tails.

Hence, it\'s half of 32%.

The answer is 16%. [ANSWER]