# Standard deviations

• Dec 7th 2010, 05:07 PM
tmas
Standard deviations
Nylon strands are manufactured to a mean tensile strength of 1.5 N, with a standard deviation of 0.04N. If the tensile strength of strands is normally distributed
a) what percentage of the strands would have a strength of less than 1.4 N, and will be recycled?
b) what range of strengths, symmetrical about the mean, would you expect 90% of the strands to be recycled?

a) I got the answer to this one. Just by using the z score formula and looking it up on the table and such its 0.62%

b) this is the question that I am having issues with
here is what i did:
area to left (looked up on table) = .9015 which is a z score of 1.29
plugged into formula
1.29 = (x-1.5)/.04
multiply both sides by .04
0.0516 = x-1.5
x = 1.5516

I know you are supposed to do something like that but i do not know how to get this "range" they are talking about.. this is probably due to the fact i have no idea what symmetrical about the mean means... i can't find the information about this anywhere..

the answer in the back of the book is 1.43N to 1.57N
-in a sense i'm sort of close...
• Dec 7th 2010, 05:55 PM
pickslides
The range will be $\displaystyle \pm a$ such that $\displaystyle P\left( Z<\frac{a-1.5}{0.04}\right) = 0.05$
• Dec 7th 2010, 06:17 PM
tmas
i'm not sure i understand...
• Dec 7th 2010, 07:41 PM
pickslides
90% symmetrical around the mean. Imagine the 100% is broken into intervals 5%-90%-5% = 0.05-0.9-0.05

Is this any better?