Question

We are using SPSS 24 IBM software to analyze, format and plot the Histogram but i need to see how the data is represented, used and Graphed on a histograph:

1.] Suppose you were to roll 2 dice of 6 sides each, and take the total. The values range from 2 - 12, and there are 36 possible combinations of the two dice.

a.] (40 pts) Create a histogram that shows the theoretical distribution of the dice rolls. Figure out how many combinations there are for each of the possible values, and enter this into SPSS. Then plot the histogram.

b.] (5 pts) What is the probability of observing a 5?

c.] (5 pts) What is the mean and standard deviation of this distribution?

d.] (10 pts) A value of 12 is how many standard deviations from the mean?

Answer 1

We are given that 2 dice of 6 sides each rolled , and we take the total. therefore there are total 36 possibilities .

Part a) The total 36 combinations on the upper face of the dice and their total is as follows :

Now we have to draw the histogram for the distribution of all totals.

So first enter the all totals into the SPSS , in the first column. to draw the histogram go to Graphs menu ---->Legacy Dialogs ----> Histogram.

Then in the Variable box just enter the column name total and click on OK.

you will get the histogram of the distribution of totals

The histogram of the distribution will look like as follow :

Part b) What is the probability of observing a 5?  

P( total is 5 ) = frequency of 5 / N

On the histogram frequency for 5 is 4, that is we got the sum 5 , 4 times.

So P( observing 5 ) = 4/35 = 0.1111

Part c)

What is the mean and standard deviation of this distribution?

As we can see on the histogram mean = 7 and standard deviation = 2.449

Part d)

A value of 12 is how many standard deviations from the mean?

We have to find z score for x = 12

z = =   =   = 2.04

z = 2.04

A value of 12 is above the 2.04 standard deviations from the mean.