Question

The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 145 and a variance of 25. The material is considered defective if the breaking strength is less than 134.5 pounds. What is the probability that a single, randomly selected piece of material will be defective

Answer 1

Standard deviation (sd) is the square root of the variance
so sd = √25 = 5

z- score = (x - mean)/sd
= (134.5-145)/5 = -2.1

now you go to your table or chart provided in your text , find -2.1 in your left column to see
.0179
so the prob is .0179

Many newer textbooks these days dealing with that topic don't even publish the tables any more, relying rather on "technology" to do the look-up

My favourite page for this is
http://davidmlane.com/normal.html
click on "below" and enter -2.1 to get the above result
The beauty of this site is that you don't even have to find the z-scores first,
in the mean, enter 145
in SD, enter 5
click on below, and enter 134.5
and behold.... .0179 !!!!!!!

Answer 2

Find the monthly payment for the loan. (Round your answer to the nearest cent.)
$800 loan for 12 months at 10%