Product designers often must consider physical characteristi

Product designers often must consider physical characteristics of their target population. For example, the distribution of heights of men aged 20 to 29 years is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer the following questions.

a)What percent of these men are taller than 74 inches?

b)Between what heights do the middle 95% of young men fall?

c)What percent of young men are shorter than 66.5 inches?

What percent of young men are between 71.5 and 74 inches?

Solution

Heights of men ~ N (69, 2.5)

P( 69 - 2.5 < X < 69 +2.5) = 68%

P( 69 - 2* 2.5 < X < 69 + 2*2.5) = 95%

P( 69 - 3* 2.5 < X < 69 + 3*2.5) = 99.7%

P( 69 - 2* 2.5 < X < 74) = 95%

a)Therefore 5% mens are tallers than 74 inches and smaller than 64 inches combinelyTherefore as normal is symmetric distribution so 2.5% of means are taller than 74 inches

b) Middle 90% men fall between (64, 74) inches

c) as P( 66.5 < X < 71.5) = 68%

Therefore 32% mens are tallers than 71.5 inches and smaller than 66.5 inches combinely

So as normal is symmetric half of 32% i.e 16% of mens are smaller than 66.5 inches

d) % of persons less than 74 - % of persons less than 71.5 = 97.5 - 84 = 13.5% of mens are between 71.5 and 74 inches