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 1.6 flaws per square yard and standard deviation 0.8 flaws per square yard. This population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 166 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 1.7 per square yard. (Round your answer to four decimal places.)

Explanation / Answer

Sol:

Since the sample size is larger than 30 (n = 166), the Central Limit Theorem applies. So,

x “sigma sub x-bar”) is the standard deviation of sample means, or standard error of the mean

=std dev/sqrt(n)=0.8/sqrt(166)

=0.062

P(X bar>1.7)=P(Z>1.7-1.6/0.062=0.1/0.062)

=P(Z>1.61)'

P ( Z>1.61 )=1P ( Z<1.61 )=10.9463=0.0537

the approximate probability that the mean number of flaws exceeds 1.7 per square yard.=0.0537

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