Question

Use the Normal model ​N(100​,16​) describing IQ scores to answer the following.

​a) What percent of​ people's IQs are expected to be over 75​?

​b) What percent of​ people's IQs are expected to be under 90​?

​c) What percent of​ people's IQs are expected to be between 112 and 124​?

Answer 1

we have N(100,16), this means and

(A) we have to find the percent of​ people's IQs are expected to be over 75, i.e. x = 75

using the formula

this gives us

{Using z distribution table}

So, 94.06% of​ people's IQs are expected to be over 75

(B) we have to find the percent of​ people's IQs are expected to be under 90, i.e. x = 90

using the formula

this gives us

   {Using z distribution table}

  

So, 26.43% of​ people's IQs are expected to be under 90

(C)we have to find the percent of​ people's IQs are expected to be between 112 and 124​, i.e. x1=112 and x2=124

using the formula

this gives us

   {Using z distribution table}

  

So, 15.98% of​ people's IQs are expected to be between 112 and 124​