Question

Assuming a particular carbon fiber strand has a mean breaking strength of 1500 psi, a standard deviation of 125 psi, and the breaking strength is approximately normally distributed, answer the following question: What is the probability that a randomly sampled carbon fiber strand put through a stress test will break before it reaches the stated quality standard of 1200 psi?

A. 0.050

B. 0.125

C. 0.008

D. 0.992

Answer 1

Let X denotes the breaking strength

Then from given data X~ N( 1500, (125)^2 )

Then we need to find the probability that a randomly sampled carbon fiber strand put through a stress test will break before it reaches the stated quality standard of 1200 psi.

That means P( X< 1200)

On standardizing Z =( X-1500)/125 ~ N(0,1)

So P(X<1200) = P( ( X-1500)/125 < (1200-1500)/125)

= P(Z< -2.4) = P(Z>2.4) because of symmetry.

= P(0<Z< infinity ) - P( 0<Z< 2.4)

= 0.5 - 0.4918

=0.0081975

=0.008

Option C

Thank you.