You have to guess if an athlete is either a basketball player or a golf player f

Question

You have to guess if an athlete is either a basketball player or a golf player from his/her height. You know that Basketball players heights are distributed according to N(80 in, 36 in^2) Golf players heights are distributed according to N(70 in, 25 in^2). a) If the athlete's height is 73 in what would be the guess that maximizes your probability of being right? b) If the athlete's height is 74 in what would be the guess that maximizes your probability of being right? c) If the athlete's height is 75 in what would be the guess that maximizes your probability of being right?

Explanation / Answer

4.3) as z score =(X-mean)/std deviation

for 73 in ; zscore for basketball player =(73-80)/6=-1.1667

for 73 in ; zscore for Golf player =(73-70)/5=0.6

as z score for golf player is near to mean, golf would be guess that maximizes probability.

b)for 74 in ; zscore for basketball player =(74-80)/6=-1

for 74 in ; zscore for Golf player =(74-70)/5=0.8

as z score for golf player is near to mean, golf would be guess that maximizes probability.

c)for 75 in ; zscore for basketball player =(75-80)/6=-0.833

for 75 in ; zscore for Golf player =(75-70)/5=1

as z score for basketball player is near to mean, basketball would be guess that maximizes probability.

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