It seems to me that the clue in this question is "normally distributed". This question is being asked from the theoretical ideal situation.
>>> "Glenn Clemens" <firstname.lastname@example.org> 6/24/2011 9:22 AM >>>
Can someone with a statistics background help me out with question 29 (82 video game players, ages normally distributed with mean 17 and std d 3; were there 15 players over the age of 20?).
Yes, in an ideal normal distribution (which I don?t think you?ll see with 82 data points), 15.9% of the scores should be more than 1 sigma above the mean. But in a sample from a normal, doesn?t this become an expected value? In the given problem, we would EXPECT about 13 players to be 20 years or older, but there could be more or there could be fewer.
Assume the 82 players were randomly sampled from a larger population whose ages are normally distributed with the given mean and std d. If I use a binomial distribution with n = 82 and p = 0.159, I get a 9.6% chance that there will be exactly 15 players over the age of 20 and a 32% chance that there will be 15 or more players over the age of 20. What then is the appropriate answer to ?Determine if there were 15 players in this study over the age of 20.?? Probably not but we can?t be even close to sure.
I do not like the wording of this question. But my probability and statistics education is a loooong time in the past. I?d appreciate a second (third, fourth, . . . dozenth) opinion.