Please use this guide as a reference for solving the problems:

This formula will take z-scores from any normal distribution and convert them to standard normal z-scores. We can then take these converted z's to the tables and find indicated probabilities, just as we did in the previous lesson.

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

For completeness' sake, the minimum usual is 70 and the maximum usual is 130.

Recall from Lesson 2 Chapter 5 that:

minimum usual =-2 =100-2(15)=70

maximum usual =-2=100+2(15)=130

Let's find the probability that a randomly selected person has an IQ less than 120.

IQ scores have a mean of 100 and a standard deviation of 15. The z-scores tables only work for the standard normal, where the mean is zero and the standard deviation is one. We must take our z of 120 and convert it to a standard normal z.

This is the formula we use to convert any z-score to a standard normal z-score.

The required standard normal z equals the score we want to convert (x) minus the mean () and then divided by the standard deviation ()

z=x -/

For this example, we want to convert 120 to a standard normal z.

x =120 =100 =15

z = 120-100/15 =20/15= 1.33

The z of 120 in the normal distribution for IQ, converts to a standard normal z of 1.33.

Now we take the 1.33 to the positive z table, as we did in the previous lesson. 1.33 leads to an area (probability) of 0.9082.

Conclusion: The probability that a randomly selected person has an IQ less than 120 equals 0.9082, 91%. We can also conclude that 91% of the population has an IQ less than 120.

Now, show your work, here are the problems:

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

1) What is the probability that a randomly selected person has an IQ of less than 90?

2) What is the probability that a randomly selected person has an IQ of more than 110?

The heights of men are normally distributed with a mean of 68.6 inches and a standard deviation of 2.8 inches.

3) What percent of men are less than 5 feet, 6 inches tall?

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

4) Find the probability of a pregnancy lasting more than 280 days.

Bonus: What is the probability of a having an IQ between 110 and 120?