Question

4. MIT is college whose members possess IQs in the top 2% of the population. If IQs are normally distributed, with mean 100 and a standard deviation of 16, what is the minimum IQ required for admission to IT? .

b)If 20 individuals were randomly selected, what is the probability that the average IQ for the group is 110?

Answer 1

a)

Mean = = 100

Standard deviation = = 16

Top 2%

P[ X > x ] = 2% = 0.02

P[ ( X - )/ > ( x - )/ ] = 0.02

P[ ( X - 100 )/ 16 > ( x - 100 )/ 16​​​​​​​ ] = 0.02

P[ Z > ( x - 100 )/ 16​​​​​​​ ] = 0.02

Also,

P[ Z > 2.54 ] = 0.02

( x - 100 )/ 16 = 2.54

( x - 100 ) = 16*2.54

x - 100 = 40.64

x = 100 + 40.64

x = 140.64

b)

The following information about the mean and standard deviation has been provided:

We need to compute . The corresponding z-value needed to be computed:

Therefore,

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