Question

Standard Normal Distribution Activity

1. Roll and record 100 rolls of four, fair six-sided dice.

2. Theoretically, the mean, median, and mode should all be 14. Check to see if this is the case. What is likely to happen to these values if the number of rolls were increased to 200? 300?   1000?

3. Using the calculator, find the standard deviation for the data.

4. Answer the following questions:

a. What percentage of the rolls were 12,13, 14,15, or 16? How does this compare to the percentage based on the z-score table using the z-scores for 11.5 and 16.5?

b. What percentage of the rolls were 10,11,12,13,14,15,16,17, or 18? How does this compare to the percentage based on the z-score table using the z-scores for 9.5 and 18.5?

c. What percentage of the rolls were 7,8,9,10,11,12,13,14,15,16,17,18, 19,20,21? How does this compare to the percentage based on the z-score table using the z-scores for 6.5 and 21.5?

d. An outlier is a data point that, on either end, is farther away from the rest of the data than we would expect. Exactly how far is open to interpretation. One definition says that any data point more than 3 standard deviations from the mean in either direction is an outlier. By this definition, does the data have any outliers?

Answer 1

Hey I have used Excel to answer your question as it is the only feasible way.

Q2)	mean	14.52
	median	15
	mode	15
Q3)	Standard deviation	3.4450374
Q4)        a)	% of 12,13, 14,15, or 16	48.00%
	using z score area is	53.20%
b)	% 10,11,12,13,14,15,16,17, or 18	80.00%
	using z score of 9.5 and 18.5 area is	80.85%
c)	% 7,8,9,10,11,12,13,14,15,16,17,18, 19,20,21	99.00%
	using z score of 6.5 and 21.5 area is	97.05%
d)	lower limit	4.1848877
	upper limit	24.855112
	no of outliers	0

now these are excel images in case you need-

not possible to show all the value

Now this image below has all the formula in excel that I have used

now the image below contains formula I used to generate dice rolls

What is likely to happen to these values if the number of rolls were increased to 200? 300?   1000?

So if increase the rolls our calculated value of mean , median and mode would tend closer to the theoretical value of 14. as our median is 15.

Now one important thing it's not necessary that if you do the same simulation in your Excel you would get the exact same results as these rolls are random every time they will generate different numbers.

I tried pasting the table of values but it's exceeding character limit .

Please upvote If I am able to help you.

Thanks