Question
In: Statistics and Probability
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
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 6.9-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 2.5% or largest 2.5%.
What is the minimum head breadth that will fit the clientele?
min =
What is the maximum head breadth that will fit the clientele?
max =
Do not round your answer.
Solutions
Expert Solution
µ = 6.9
σ = 1.1
proportion= 0.95
proportion left 0.05 is equally
distributed both left and right side of normal
curve
z value at 0.025 = ±
1.960 (excel formula =NORMSINV(
0.05 / 2 ) )
z = ( x - µ ) / σ
so, X = z σ + µ =
X1 = -1.960 * 1.1
+ 6.9 = 4.744
X2 = 1.960 * 1.1
+ 6.9 =
9.056
so,
min = 4.74
max = 9.06
orchestra answered 1 year agoRelated Solutions
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