Question

The amount people pay for electric service varies quite a bit, but the mean monthly fee is $168 and the standard deviation is $34. The distribution is not Normal. Many people pay about $90 in rural areas of the country and about $150 in urban areas of the country, but some pay much more. A sample survey is designed to ask a simple random sample of 1,200 people how much they pay for electric services. Let x̄ be the mean amount paid.

Part A: What are the mean and standard deviation of the sample distribution of x̄? Show your work and justify your reasoning.

Part B: What is the shape of the sampling distribution of x̄? Justify your answer.

Part C: What is the probability that the average electric service paid by the sample of electric service customers will exceed $170? Show your work.

Answer 1

Mean = = 168

Standard deviation = = 34

Sample size = 1200

Part A:

Mean = = 168

Standard deviation =

Part B.

Here sample size is large, by using central limit theorem we say that it is going to be a normal distribution. Shape of the normal distribution is bell shape.

Part C.

We have to find P( > 170)

For finding this probability we have to find z score.

That is we have to find P(Z > 2.04)

P(Z > 2.04) = 1 - P(Z < 2.04) = 1 - 0.9792 = 0.0208

( From z table)

The probability that the average electric service paid by the sample of electric service customers will exceed $170 is 0.0208