The amount people pay for cable service varies quite a bit, but the mean monthly

Question

The amount people pay for cable service varies quite a bit, but the mean monthly fee is $142 and the standard deviation is $29. The distribution is not Normal. Many people pay about $76 for basic cable and about $160 for premium service, but some pay much more. A sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. Let x be the mean amount paid.

Part A: What are the mean and standard deviation of the sample distribution of x? Show your work and justify your reasoning. (4 points)

Part B: What is the shape of the sampling distribution of x? Justify your answer. (2 points)

Part C: What is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

Explanation / Answer

a) mean of the sample distribution =142

And standard deviation of the sample distribution of x =std deviation/(n)1/2 =29/(1500)1/2 =0.7488

B)

from central limit theorum if sample size is greater than 30 then sampling distribution of sample mean will follow normal distribution irrespective of distribution of population

therefore  shape of the sampling distribution of x will be approximately normal

c)

for normal distribution z score =(X-)/ here mean=       = 142.000 std deviation   == 29 sample size       =n= 1500 std error=x=/n= 0.7488 probability = P(X>143) = P(Z>1.34)= 1-P(Z<1.34)= 1-0.9091= 0.0909

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