Question

Find the I.Q (Intelligence Quotient ) that is the 67th percentile in a population of I.Q scores that is Normally distributed with mean 110 and standard deviation 12:

Answer 1

Here Z is the standard normal variable

Let c be the I.Q that is the 67th percentile

As c from a population of I.Q scores that is Normally distributed with mean 110 and standard deviation 12

so, will follow standard normal

67th percentile means 67% data lies below the IQ that is 67th percentile

so, probability = 67%/100% = 0.67

Now we get the equation

From z table we get the value of

so, c = 115.28

Answer: The I.Q that is the 67th percentile in a population is 115.28