You are in charge of reviewing the IQs of military personnel

You are in charge of reviewing the IQs of military personnel stationed at Rota.You know that IQ scores are normally distributed with a mean of 100 and standard deviation of 15.Base housing has 200 occupants and you have determined that results of their IQ testing mimic the population as a whole.At a briefing your colonel wants to know how many of these soldiers have an IQ of

At least 100

Between 85 and 115

Not more than 70

What answers do you provide the colonel?

Solution

You are in charge of reviewing the IQs of military personnel stationed at Rota.You know that IQ scores are normally distributed with a mean of 100 and standard deviation of 15.Base housing has 200 occupants and you have determined that results of their IQ testing mimic the population as a whole.At a briefing your colonel wants to know how many of these soldiers have an IQ of

At least 100

Z value for 100, z=(100-100)/15 =0

P( x>=100) P(z >0) =0.5

The number of people = 200*0.5 =100

Between 85 and 115

Z value for 115, z=(115-100)/15 =1

Z value for 85, z=(85-100)/15 = -1

P( 85 <x<115) = P(-1<z<1) = 0.8413 - 0.1587 =0.6826

The number of people = 200*0.6826 =136.52

The number of people = 137 (rounded)

Not more than 70

Z value for 70, z=(70-100)/15 = -2

P( x <70) P(z < -2) = 0.0228

The number of people = 200*0.0228 =4.56

The number of people = 5 (rounded)

What answers do you provide the colonel?

Majority of the people are having IQ between 85 and 115.