The winner of a tennis trophy for "best serve" is the league player with the highest first serve percentage during games played. The three players with the highest first serve percentages are players A, B, and C. Player A landed 62% of first serves, player B landed 0.7 of first serves and player C landed 3350 of first serves. Graph an inequality that represents the possible first serve percentages (in decimal form) for the other players in the league. (Assume there are no players with the same first serve percentage.)

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irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

#12 the answer is the third option