Question

he amount people who pay for cell phone service varies quite a bit, but the mean monthly fee is $55 and the standard deviation is $22. The distribution is not Normal. Many people pay about $30 for plans with 2GB data access and about $60 for 5GB of data access, but some pay much more for unlimited data access. A sample survey is designed to ask a simple random sample of 1,000 cell phone users how much they pay. 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 cell phone service paid by the sample of cell phone users will exceed $56? Show your work. (4 points)

Answer 1

Solution :

Mean = = 55

Standard deviation = = 22

Sample size = 1000

Part A:

Mean = = 55

Standard deviation =

= / n = 22 / 1000 = 0.6957

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( > 56)

For finding this probability we have to find z score.

Z= p [(x - ) / ] =(56 -55) /0.6957 ]

That is we have to find P(Z > 1.44)

P(Z > 1.44) = 1 - P(Z < 1.44) = 1 - 0.9250663 =0.0749337 = 0.0749

( From z table)

The probability that the average electric service paid by the sample of electric service customers will exceed $170 is 0.0749.

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