The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 145 and a variance of 4. The material is considered defective if the breaking strength is less than 140 pounds. What is the probability that a single, randomly selected piece of material will be defective? (You may need to use the standard normal distribution table. Round your answer to four decimal places.)

Question

145-140=5 is below mean 25=5 10/5= -2
answer 0.9988 thank you for your time and I hope you had a nice weekend.

Answer 1

variance of 4 means std of 2.
5 is below the mean by 2.5 std.
P(Z < -2.5) = .0062 = 0.62%

Think about it. Your answer indicates that virtually all of the pieces are defective. That would surely not ever be tolerated in a real-world situation.

Take a visit to

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

and you can play around with this Z-table stuff.

Answer 2

Thank you Steve