The number of flaws per square yard in a type of carpet material varies with mea

Question

The number of flaws per square yard in a type of carpet material varies with mean 1.4 flaws per square yard and standard deviation 1.2 flaws per square yard. This population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 172 square yards of the material, records the number of flaws found in each square yard, and calculates x, the mean number of flaws per square yard inspected. Use the central limit theorem to find the approximate probability that the mean number of flaws exceeds 1.5 per square yard. (Round your answer to four decimal places.)

Explanation / Answer

here from central limit theorum

mean number of flaws in 172 square yard =1.4

and std error of mean =population std deviation/(n)1/2 =1.2/(172)1/2 =0.0915

therefore from normal approximation:

approximate probability that the mean number of flaws exceeds 1.5 per square yard

=P(X>1.5)=P(Z>(1.5-1.4)/0.0915)=P(Z>1.0929)=1-P{Z<1.9029)=1-0.8628 =0.1372

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