A Stat Geek’s Take
on the Classic
Shake and Score
Dice Game!
In this game, you can forget everything you know about the classic game of Yahtzee. The only thing the two
games have in common is the dice and a score sheet. But the winners get a prize!
1. First, consider rolling a fair die one time. There are six possible outcomes. List the outcomes and the
probability of obtaining each outcome on a single roll in the table below. Convert the probabilities to a
fraction, rounding to two decimal places.
Outcome
Probability
In the grid below, draw a bar chart of this probability distribution with the outcomes on the x-axis, and the
height of the bars equal to the probability of each outcome.
Guess the mean of this
distribution
0.18
0.16
_______________
0.14
0.12
0.08
Guess the standard
deviation of this
distribution
0.06
_______________
0.10
0.04
0.02
Roll your die one time.
Record the outcome
0.00
_
0
1
2
3
4
5
6
______________
2. Consider rolling a fair die twice and averaging the outcome. There are eleven possible outcomes. List the
outcomes and the probability of obtaining each outcome in the table below (Hint: to obtain the probabilities,
use the chart for all outcomes of two rolls of the die at the end of this worksheet to determine how often each
outcome occurs). Convert the probabilities to a fraction, rounding to two decimal places.
Outcome
Probability
In the grid below, draw a bar chart of this probability distribution with the outcomes on the x-axis, and the
height of the bars equal to the probability of each outcome.
0.18
Guess the mean of this
distribution
0.16
_______________
0.14
0.12
0.10
Guess the standard
deviation of this distribution
0.08
_______________
0.06
0.04
Roll your die twice. Record
the average value of the
two rolls
0.02
0.00
0
1
2
3
4
5
6
_______________
3. Consider rolling a fair die five times and averaging the outcome. The possible outcomes are numerous, and it
would take too long to figure these out.
Guess the mean of the distribution _______________
Guess the standard deviation of the distribution _______________
Roll your die five times. Record the average value of the rolls _______________
4. Consider rolling a fair die ten times and averaging the outcome. The possible outcomes are numerous, and it
would take too long to figure these out.
Guess the mean of the distribution _______________
Guess the standard deviation of the distribution _______________
Roll your die ten times. Record the average value of the rolls _______________
Final Score: Sum the four average values of the rolls above and write this value in the box.
Hint for number 2: Outcomes of two rolls of die