Discrete Math Section 17.4 Recognize various types of distributions. Apply normal distribution properties. A normal distribution is a bell shaped curve. Properties of a normal distribution 1. About 68% of the data is within one standard deviation of the mean. 2. About 95% of the data is within two standard deviations of the mean. 3. About 99% of the data is within three standard deviations of the mean.

The standard normal distribution is the normal distribution having a mean of zero and a standard deviation of one. Its graph is called the standard normal curve. The equation of the standard normal curve is :. The area under the curve is one. The area under the curve to the left of a number z is the proportion of the data having standard values less than z. Shaded area = P(z) = proportion of the data less than z.

The value of P(z) is called a percentile. A percentile indicates the percent of people who scored lower than someone with a standard value of z. See table on page 664 ww.measuringusability.com/pcalcz.php Find P(-2.1) Find P(-.6) Find P(1.8)

On a test the mean score was 75 and the standard deviation was 8. Find the percent of students that scored less than 87. To find percentiles (the percent of the data less than the z score) using normal distributions 1. menu 2. statistics 3. distributions 4. normal Cdf 5. lower bound = 0 6. upper bound = 7. μ = 0 8. ϭ = 1

In a reaction test the responses were normally distributed with a mean of 12 seconds and a standard deviation of 2.5 seconds. Find the percent of test subjects whose reaction times were between 5 and 8 seconds. To find the percent of the data between two z scores using normal distributions 1. menu 2. statistics 3. distributions 4. normal Cdf 5. lower bound = 6. upper bound = 7. μ = 0 8. ϭ = 1

On a standardized test, the mean was 70 and the standard deviation was 4. What score would you have to make in order to score at the 90 th percentile? To find the z score based on the percentile (area under curve) 1. menu 2. statistics 3. distributions 4. inverse Normal 5. Area = 6. μ = 0 7. ϭ = 1

Assignment Page 667 Problems 1,4,6,8,10,11,12,14,15