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 178 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, the sampling distribution of sampling mean is normal distribution irrespective of population shape.

= 1.8

= 0.9

n = 178

SE = /

= 0.9/

= 0.0675

To find P(>1.9)

Z = (1.9 - 1.8)/0.0675

= 1.4824

Table gives area = 0.4306

So,

P(>1.9) = 0.5 - 0.4306 =0.0694

So,

Answer is:

0.0694