The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 115 and a variance of 25. The material is considered defective if the breaking strength is less than 105 pounds. What is the probability that a single, randomly selected piece of material will be defective?

Answer 1

difference from mean = 115-105 = 10 below mean

variance = 25 so standard deviation = 5

so z = -10/5 = -2

it is two standard deviations below mean

for z = 2 look up in normal table

http://davidmlane.com/hyperstat/z_table.html

probability = .0228

Answer 2

So your graph is going to have a mean of 115 and your standard deviation is 5 (because variance is standard deviation squared). From here you can just plug in your calculator. Since the graph is "normally distributed" you can use normalcdf(left interval, right interval, mean, sd) You want to find the probability for anything less than 105 pounds so that means normalcdf(-99999,105,115,5)=.023