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