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

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!

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