If you are an engineer that designs motorcycle helmets for men you must consider

Question

If you are an engineer that designs motorcycle helmets for men you must consider the breadths of a man's head. After considerable research you found men have head breadths that are normally distributed with a mean of 5.9 inches and a standard deviation of 1.2 inches. This morning you are told about financial constraints and you must design the helmets to fit all men except those that have head breadths that are in the smallest or largest 2.8% of the population. What are the minimum and maximum head breadths that the helmets will fit?

Explanation / Answer

mean = 5.9

std. dev. = 1.2

For 2.8%, left/right tailed z-value = +/- 1.911

minimum head breadths = mean - z*std. dev. = 5.9 - 1.911*1.2 = 3.6068

maximum head breadths = mean + z*std.dev = 5.9 + 1.911*1.2 = 8.1932

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