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. (4 points) Part B: What is the shape of the sampling distribution of x̄? Justify your answer. (2 points) 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. (4 points) (10 points)

Answer 1

Given that ,

mean = = 168

standard deviation = = 34

A) n = 1200

= = 168

= / n = 34 / 1200 = 0.9815

B) The probability distribution of x is approximately normal with μ_x = 168 and σ_x = 0.9815

c)

P(x >170 ) = 1 - p( x< 170)

=1- p [(x - ) / < (170 -168) /0.9815 ]

=1- P(z < 2.04 )

= 1 - 0.9793 = 0.0207

probability = 0.0207