Suppose that the average IQ score is normally distributed wi

Suppose that the average IQ score is normally distributed with a mean of 150 and a standard deviation of 23. In addition to providing the answer, state the relevant Excel commands. (Use Excel)

What is the probability a randomly selected person will have an IQ score of less than 80? (Round your answer to 4 decimal places.)

What is the probability that a randomly selected person will have an IQ score greater than 110? (Round your answer to 4 decimal places.)

What minimum IQ score does a person have to achieve to be in the top 1.5% of IQ scores? (Round your answer to 2 decimal places.)

Solution

a)

We can use the NORMDIST function here.

=NORMDIST(80, 150, 23, 1)

= 0.001169302 [answer]

b)

As NORMDIST gives the left tailed area, we get its complement to get the right tailed area. Thus,

=1-NORMDIST(110, 150, 23, 1)

=0.958994089 [answer]

c)

As it is the top 1.5%, then the left tailed area is 1 - 0.015 = 0.985. Thus, we use the NORMINV function,

=NORMINV(0.985, 150, 23)

=199.9120787 [answer]