Suppose that you are a student worker in the Statistics Department, and they agr

Question

Suppose that you are a student worker in the Statistics Department, and they agree to pay you using the Random Pay system. Each week the Chair flips a coin. If it comes up heads, your pay for the week is $80, and if it comes up tails, your pay for the week is $40. You work for the department for two weeks. Let be the average of the pay you receive for the first and second week. The sampling distribution of x is:

a) exactly normal with mean $60 and standard deviation 14.14

b) given by the following probability distribution

probability: .25 .50 .25

c) approximetley normal with mean $60 and standard deviation 14.14

Explanation / Answer

it is discrete so it can't be normal, even though you might try approximating it with a normal distribution when you look at it over a period of time.

so the answer is
given by the following probability distribution.
Probability: 0.25 0.50 0.25

as you increase the number of weeks you will find that the distribution will become approximately normal with a mean of $60 and a standard deviation of $20 divided by the square root of N, but that does not work for N = 2

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