SOLUTION: I don't get this: could you please help me to figure this out? What is the breaking strength of a ertain new synthetic is normailly distributed,with a mean of 135,variance of 4. Ma

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Question 849800: I don't get this: could you please help me to figure this out? What is the breaking strength of a ertain new synthetic is normailly distributed,with a mean of 135,variance of 4. Material is defective if the breaking strength is less than 130.8 pounds. What is the probability that a single,randomly selected piece of material will be defective( round to four decimals).
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
mean = m = 135
variance = s^2 = 4
standard deviation is equal to the square root of the variance which is equal to 2.
standard deviation = s = 2

z-score is equal to (x-m) / s

x is the score you are testing.
m is the mean of the population.
s is the standard deviation of the population.

you calculate the z-score and then you look up the z-score in the table to find the probability that the area under the curve in the normal distribution will be less then that z-score.

in your problem:

x = 130.8

with m = 135 and s = 2, the z-score will be equal to (130.8 - 135) / 2 which is equal to -2.1.

looking this z-score up in the z-score table, tells you that the probability of getting a score less than -2.1 is equal to .0179

the z-score table i used can be found at the following link:

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut40_ratgraph.htm

a picture of what the table looks like and how the value was obtained is shown below:

check the link to see the picture on top of the table that shows you what area of the distribution curve is being found through use of the table.

it's the area to the left of the z-score.