Q:

Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 1.1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 0.5% or largest 0.5%. What is the minimum head diameter that will fit the clientele? min = What is the maximum head diameter that will fit the clientele? max = Remember to round your z-scores to 2 decimal places. Enter your final answer as a number accurate to 1 decimal place.

Accepted Solution

A:
Z =(x - μ)/σ Zσ = x - μ Zσ + μ = x x = Zσ + μ from Z-Table: Given P(xZ) = 0.005, Z=2.58 x = Zσ + μ x = (2.58)(1.1) + 6.4 x = 9.238 Thus, min = 3.6-in max = 9.2-in