SOLUTION: The mean number of flaws per square yard in a type of carpet material is claimed to be 2.2 flaws per square yard along with a standard deviation of 1.2 flaws per square yard. The

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Question 885338: The mean number of flaws per square yard in a type of carpet material is claimed to be 2.2 flaws per square yard along with a standard deviation of 1.2 flaws per square yard. The population can be assumed to be normal.
Find P(X ≤ 4), the percentage of time there are fewer than 4 flaws per square yard.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
m = mean
sd = standard deviation
x = raw score
z = z score
you get:
m = 2.2
sd = 1.2
x = 4
population is assumed to be normal.
z score is equal to (x-m)/sd
replace x with 4 and m with 2.2 and sd with 1.2 and you get:
z score is equal to (4 - 2.2) / 1.2 = 1.5
you are looking for the area under the normal distribution curve that is to the left of a z score of 1.5
look up the z score in the z score table and you will see that the area to the left of that z score is equal to .9332
this means that the percentage of time that there are fewer than 4 flaws per square yard of carpet material is 93.32%.