Solution Found!
Full answer: Section II: Free Response Show all your work. Indicate clearly the methods
Chapter 7, Problem T7.12(choose chapter or problem)
The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $38 and the standard deviation is $10. The distribution is not Normal: many households pay a base rate for low-speed access, but some pay much more for faster connections. A sample survey asks an SRS of 500 households with Internet access how much they pay. Let x be the mean amount paid.
(a) Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds $39.
(b) What are the mean and standard deviation of the sampling distribution of x ?
(c) What is the shape of the sampling distribution of x ? Justify your answer.
(d) Find the probability that the average fee paid by the sample of households exceeds $39. Show your work.
Questions & Answers
QUESTION:
The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $38 and the standard deviation is $10. The distribution is not Normal: many households pay a base rate for low-speed access, but some pay much more for faster connections. A sample survey asks an SRS of 500 households with Internet access how much they pay. Let x be the mean amount paid.
(a) Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds $39.
(b) What are the mean and standard deviation of the sampling distribution of x ?
(c) What is the shape of the sampling distribution of x ? Justify your answer.
(d) Find the probability that the average fee paid by the sample of households exceeds $39. Show your work.
ANSWER:Step 1 of 4
a)
To determine the probability for a single household, we require the knowledge of the population distribution.
However, we only know the mean and the standard deviation of the population, while the population distribution is not Normal. The (shape of the) population distribution is unknown as we only know it is not Normal and thus we cannot determine the probability.