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 7.1-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.1% or largest 2.1%.

What is the minimum head breadth that will fit the clientele?

min =

What is the maximum head breadth that will fit the clientele?

max =

show work on how to obtain z score on the calculator. Step by step.

Answer 1

Let X is a random variable shows the head breadths. Here X has normal distribution with following parameters

Now we need z-score that has 0.021 area to its left. Using z table, z-score -2.03 has approximately 0.021 area to its left. So required  minimum head breadth that will fit the clientele is

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Now we need z-score that has 0.021 area to its right. Using z table, z-score 2.03 has approximately 0.021 area to its right. So required  maximum head breadth that will fit the clientele is