Question

13. Adult IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly chosen adult has an IQ between 70 and 115.

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 100

= 15

P(70 < x< 115)

= P(X < 115) - P(X < 70)

=  P[(X - )/ <  (115 - 100)/15] -   P[(X - )/ <  (70 - 100)/15]

= P[Z < 1.00] - P[Z < -2.00]

= 0.8413 - 0.0228 ..Use z table

= 0.8185

Required Probability = 0.8185