Question

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Find the probability, rounded to four decimal digits, that the person has an IQ greater than 120. Below is a sketch of the normal curve showing the area to be determined

Answer 1

The probability that the person has an IQ greater than 120 is 0.2524 of 25.24%

What is probability?

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

probability that the person has an IQ greater than 120,

P(x >120)

= P(Z > 120-100/ 15)

= P(Z > 0.667)

 P(x >120) = 1-  P(Z <  0.667)

                  = 1-0.7476

                 = 0.2524

                = 25.24%

Hence, the probability is 0.2524.

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