Question

The number of flaws per square yard in a type of carpet material varies with mean 1.8 flaws per square yard and standard deviation 0.9 flaws per square yard. This population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 168 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 1.9 per square yard. (Round your answer to four decimal places.)

Answer 1

By Central Limit Theorem, even though the population is not normal, for large samples, the sampling distribution of sample means is normal.

= 1.8

= 0.9

n = 168

SE = /

= 0.9/ = 0.0694

To find P(> 1.9):
Z = (1.9 - 1.8)/0.0694 = 1.44

Table of Area Under Standard Normal Curve gives area = 0.4251

So,

P(>1.9) = 0.5 - 0.4251 = 0.0749

So,

Answer is:

0.0749