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 1.5 flaws per square yard and standard deviation 1 flaws per square yard. This population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 174 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 1.6 per square yard. (Round your answer to four decimal places.)

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    1.6      
u = mean =    1.5      
n = sample size =    174      
s = standard deviation =    1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.319090596      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.319090596   ) =    0.093569413 [ANSWER]

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