Question

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15 what is the probability that a randomly selected person has an iq above 126

Answer 1

So we are given the mean and the s.d.. The mean is 100 and the sd is 15 and we are trying the select a random person who has an I.Q. of over 126. So our first step is to use our z-score equation:

z = x - mean/s.d.

where x is our I.Q. we are looking for

So we plug in our numbers and we get:

126-100/15 = 1.73333

Next we look at our z-score table for our P-value and I got 0.9582

Since we are looking for a person who has an I.Q. higher than 126, we do 1 - P. So we get

1 - 0.9582 = 0.0418

Since they are asking for the probability, we multiply our P-value by 100, and we get 

0.0418 * 100 = 4.18%

And our answer is

4.18% that a randomly selected person has an I.Q. above 126
Hopes this helps!