# Probability

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Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) to play this game.

a. Find the distribution of the winnings for this game.

b. The amount won is a (discrete, continuous) variable.

c. Find the expected (mean) winnings for this game.

d. Find the standard deviation of the winnings for this game.

e. Suppose you played this game 100 times. Find the mean and standard deviation for the sample mean winnings.

f. The result used in part e. is the ______________________.

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##### Solution Summary

Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) to play this game.

a. Find the distribution of the winnings for this game.

b. The amount won is a (discrete, continuous) variable.

c. Find the expected (mean) winnings for this game.

d. Find the standard deviation of the winnings for this game.

e. Suppose you played this game 100 times. Find the mean and standard deviation for the sample mean winnings.

f. The result used in part e. is the ______________________.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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