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 1.8 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 162 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.)

Explanation / Answer

here for poisson distribution meanflaws per square yard =1.8 =std deviaiton

threfore mean flaws per yard in 162  square yards =1.8

and std error of mean =1.8/(162)1/2 =0.1414

applying normal approximation of poisson distribution:

probability that the mean number of flaws exceeds 1.9 per square yard:

for normal distribution z score =(X-)/ here mean=       = 1.8 std deviation   == 1.8000 sample size       =n= 162 std error=x=/n= 0.1414

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