The following 5 questions are based on this information. (B verzion)

Data from a Survey show customers spend an average of ()$508 a yearfor broadband internet services. The standard deviation of annual internet spending is() $132. The random variable, yearly internet spending, is denoted by X.

We plan to select a random sample of 200 broadband internet customers.

1) The sampling distribution of X

Group of answer choices

a) is normal due to the Central Limit Theorem

b)is normal due to the Chebyshev's Theorem

c) is not normal because the sample size is too small

d)is not normal because the sample size is too large

explain your reasoning

2) The standard error (SE) ofX is

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3) What is the probability that a random sample of 200 broadband internet customers will provide an average(X) that is within $25 of the population mean ()?

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4) The probability in the PRECEDING question would ------ if we were to increase the sample size (n) from 200 to 251.

a)increase

b)decrease

c) stays the same

d) be zero

explain your reasoning

5) Suppose we reduce the sample size (n) from 200 to 25. The sampling distribution of Xwill be normal only if

x is...

explain your reasoning

please show step by step, equations . dumbproof it to the best of your ability

please dont type like this P[ |X(bar)-| <25] =P[ |(X(bar)-)/(/sqrt(n))| <25>