Normal Probability Distribution Prob Set-up

[mommaT2u]

I am having a difficult time figuring out how to set-up the following problem...under the problem I'll post what I thought it should be; which is wrong of course!

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. 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 the largest 2.5%. Find the minimum and maximum head breadths that the helmets will fit.

I thought I should set-up the problem as such: P(-2.5 < x < 2.5) which I would convert to P(z < -2.5) - P(z < 2.5). With working out from there to find the z Score and subtract accordingly, I was sooo far off.

Thank you in advance for your help.
Momma T

 

[galactus]

They give you the percentage. Look up .025 and -.025 in the body of the table and see what the corresponding z scores are.

There is 2.5% on each end. 5% in all. This is a 95% confidence interval.

So, we can do this and solve for x to find the breadths of the heads.

The z-score for 2.5% is -1.96. The z-score for 97.5% is 1.96.

\(\displaystyle -1.96=\frac{x-6}{1}\Rightarrow x=4.04, \;\ \text{minimum}\)

\(\displaystyle 1.96=\frac{x-6}{1}\Rightarrow x=7.96, \;\ \text{maximum}\)