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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 2 years ago
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