Assuming the IQ of football players are symmetrically distri

Assuming the IQ of football players are symmetrically distributed with a m = 100 and a s = 10, what percent of the players would have IQ

Solution

a. Greater than 120?

P(X>120) = P((X-mean)/s >(120-100)/10)

=P(Z>2) =0.0228 (from standard normal table)

b. Between 90 and 100?

P(90<X<100) = P((90-100)/10 <Z< (100-100)/10)

=P(-1<Z<0) =0.3413

c. Between 95 and 105?

P(95<X<105) = P((95-100)/10 <Z< (105-100)/10)

=P(-0.5<Z< 0.5)

=0.3829

d. Not more than 100?

P(X<100) = P(Z<(100-100)/10)

=P(Z<0) = 0.5

e. Less than or equal to 75?

P(X<=75) = P(Z<(75-100)/10)

=P(Z<-2.5) =0.0062

f. The Cleveland Browns have decided they do not want players with IQ\'s that fall in the bottom 20%. Therefore, what would the minimum IQ of a Brownie be?

P(X<c)=0.2

--> P(Z<(c-100)/10) =0.2

--> (c-100)/10 =-0.84 (from standard normal table)

--> c= 100-0.84*10 =91.6

g. On the other hand the Dallas Cowboys don\'t want players with too low or too high IQ\'s. They have restricted their draft choices to players that are in the middle 80% of IQ\'s. Therefore, would the \"Boys\" draft Ima Runningback whose IQ is 90? How about defensive lineman, Soft Underbelly whose IQ is 120?

Given a=0.2, Z(0.1)=1.28 (from standard normal table)

So the middle 80% of IQ is

mean +/- Z*s

--> 100 +/- 1.28*10

--> (87.2, 112.8)

Since the interval includes 90, the \"Boys\" draft Ima Runningback whose IQ is 90

Since the interval does not include 120, it defensive lineman that Soft Underbelly whose IQ is 120