According to the 68-95-99.7 rule, we expect 95% of head breadths to be between ____and _____ inches...

Question

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 5.6 inches and a standard deviation of 1.1 inches.

According to the 68-95-99.7 rule, we expect 95% of head breadths to be

between  ____and _____ inches.

Answer 1

95% are between 2 standard deviations so between the mean ± 2 std dev:

minimum: 5.6 - 2(1.1) = 5.6 - 2.2 = 3.4

maximum: 5.6 + 2(1.1) = 5.6 + 2.2 = 7.8

So 95% of head breadths are between 3.4 and 7.8 inches

Answer 2

We have provided, mean of 5.6 inches and a standard deviation of 1.1 inches.

so, mean=5.6 and std dev.=1.1 inches.

95% are between 2 standard deviations so between the mean ± 2 *std dev.

so lower bound= mean - 2*std dev = 5.6 - 2* 1.1 = 3.4 inches

upper bound = mean + 2*std dev = 5.6 + 2* 1.1 = 7.8 inches

According to the 68-95-99.7 rule, we expect 95% of head breadths to be

between 3.4 and 7.8 inches.