```Date: Jun 24, 2011 9:22 AM
Author: Glenn Clemens
Subject: A2/Trig #29

Can someone with a statistics background help me out with question 29 (82video game players, ages normally distributed with mean 17 and std d 3; werethere 15 players over the age of 20?). Yes, in an ideal normal distribution (which I don't think you'll see with 82data points), 15.9% of the scores should be more than 1 sigma above themean.  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 orolder, but there could be more or there could be fewer.   Assume the 82 players were randomly sampled from a larger population whoseages are normally distributed with the given mean and std d.  If I use abinomial distribution with n = 82 and p = 0.159, I get a 9.6% chance thatthere will be exactly 15 players over the age of 20 and a 32% chance thatthere will be 15 or more players over the age of 20.  What then is theappropriate answer to "Determine if there were 15 players in this study overthe 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 andstatistics education is a loooong time in the past.  I'd appreciate a second(third, fourth, . . . dozenth) opinion. Glenn Clemens
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