Construct the frequency distribution for the outcomes

Question

Discussion:

Q: The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 180 times. (Yes, the author has too much free time.) The results are given in the frequency distribution in the margin. Construct the frequency distribution for the outcomes that you would expect from a die that is perfectly fair and unbiased. Does the loaded die appear to differ significantly from a fair die that has not been "loaded?"

Outcome Frequency
1 24
2 28
3 39
4 37
5 25
6 27