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 5.6-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 breadths that are in
the smallest 3.2% or largest 3.2%.
What is the minimum head breadth that will fit the clientele?
min =
What is the maximum head breadth that will fit the clientele?
max =
Enter your answer as a number accurate to 1 decimal place.
**please include what functions you're putting into the calculator if possible (normcdf, invnorm)
Given that,
mean = = 5.6
standard deviation = = 1.1
Using standard normal table
1) P(Z < z ) 3.2%
P(Z <z ) = 0.032
z = - 1.85
Using z-score formula,
x = z * +
x = - 1.85 * 1.1 + 5.6
x = 3.6.
min. = 3.6.in.
2) P(Z > z) = 3.2%
1 - P( Z < z ) = 0.032
P( Z < z ) = 1 - 0.032
P(Z < z ) = 0.968
z = 1.85
Using z-score formula,
x = z * +
x = 1.85 * 1.1 + 5.6
x = 7.6
max. = 7.6. in.
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