# Discrete Probability Distributions

2 Questions

QUESTION 1 of 2

Dear Professor, I came across two more questions as I was studying.

For Now You Try It Section 4.2 Discrete Random Variables

For Number one the part that asks if it would be unusual for someone to roll 3 or 4 sevens out of four rolls how do you know to use within 2 standard deviations of the mean? And on the test will you speficy by saying capture 75%? Also how do we know whether we use a z-score or chevy's theorem or empirical to figure out if it is unusual?

Problem 1:

A pair of six-sided die is rolled four times. We record the number of sevens rolled

over the four rolls. Calculate the standard deviation for the number of sevens

rolled. Would it be unusual for someone to roll 3 or 4 sevens out of four rolls?

Solution:

The standard deviation is: Ïƒ = 0.746 . Based on the following interval it

would be unusual to roll more than two sevens out of four rolls:

( 2 , 2 ) (0.667 2*0.746,0.667 2*0.746) ( 0.825, 2 Âµ Ïƒ Âµ Ïƒ âˆ’ + = âˆ’ + = âˆ’ .159) .

For Problem 2:

I am not sure what information to use to go about finding the standard deviation?

Converting the above probability distribution into a game, players can risk $4 to bet

that a seven will not be rolled in four throws of the dice. If the player wins, he will

be paid $7 (a three-dollar profit), but if the player loses he/she loses his/her $4 bet.

What is the expected value for this game? Is this a smart bet to make in the long

run?

Solution:

The standard deviation isÏƒ = 3.50 , but this is not very useful since there are

only two outcomes for a trial. We know either a person will win 3 dollars

or will lose 4 dollars. The standard deviation is not needed to capture the

variation. It is easier to see the variation by simply viewing the win and

loss probabilities.

Thank you.

QUESTION 2 of 2

Hi professor, I am confused how to find the standard deviation in the problems in 4.1, number 7 i get that the mean is 1.5 but for the formula for standard deviation i am having trouble doing. Because the formula says the square root of NxPx (1-p)= the standard deviation. So what would I put for N? 4 each time? and for P what would I use?