3 Decision policy (20 points) You have to guess if an athlete is either a basket

ID: 3218016 • Letter: 3

Question

3 Decision policy (20 points)

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(80in, 36in^2 )

• Golf players heights are distributed according to N(70in, 25in^2 ).

a) If the athlete’s height is 73in what would be the guess that maximizes your probability of being right?

b) If the athlete’s height is 74in what would be the guess that maximizes your probability of being right?

c) If the athlete’s height is 75in what would be the guess that maximizes your probability of being right?

let height=x and we use stanard normal variate z=(x-mean)/sd

z1 is for basketball player and z2 is golf player.

here the minimum absolute value of z will belong to the that sportos

(a) for x=73, z1=(73-80)/6=-1,67 and z2=(73-70)/5=0.6, since absolute value of z2 is less than z1 so this player will belong to golf

(b) for x=74, z1=(74-80)/6=-1,67 and z2=(74-70)/5=0.6, this player belong to golf

(c)for x=75, z1=(75-80)/6=-1,67 and z2=(75-70)/5=0.6, this player belong to basketball

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