1. Homework Questions

2. Normal Distributions

3. Normal Curve  Sometimes called the “Bell Curve”  Used to predict outcomes of many types of events (probabilities that things will happen)

4. Properties of the Normal Curve  Bell-shaped  Symmetric  X-axis is a horizontal asymptote  Area under the curve = 1  Maximum value occurs at the mean  Because it is symmetric, the mean, median, and mode all have the same value…called the center.  Greek letter is used to represent the mean  is used for standard deviation

5. Example 1  A paper in Animal Behavior gives 11 sample distances, in cm, which a bat can first detect a nearby insect. Assume the population is normally distributed. 62, 23, 27, 56, 52, 34, 42, 40, 68, 45, 83 a) Compute the mean and standard deviation. b) Draw a normal curve for this distribution.

6. The Empirical Rule

7.  68% of the data are within one standard deviation of the mean  95% of the data are within two standard deviations of the mean  99.7% of the data are within three standard deviations of the mean

8. Example 2  A pair of running shoes lasts on average 450 miles, with a standard deviation of 50 miles. Use the empirical rule to find the probability that a new pair of running shoes will have the following lifespans. 1. Between 400-500 miles 2. More than 550 miles

9. Example 3  A survey of 1000 U.S. gas stations found that the price charged for a gallon of regular gas can be closely approximated by a normal distribution with a mean of $1.90 and a standard deviation of $0.20. How many of the stations charge a. between $1.50 and $2.30 for a gallon of regular gas? b. less than $2.10 for a gallon of regular gas? c. more than $2.30 for a gallon of regular gas?

10. Example 4  A vegetable distributor knows that during the month of August, the weights of its tomatoes were normally distributed with a mean of 0.61 pound and a standard deviation of 0.15 pound. a. What percent of the tomatoes weighed less than 0.76 pound? b. In a shipment of 6000 tomatoes, how many tomatoes can be expected to weigh more than 0.31 pound? c. In a shipment of 4500 tomatoes, how many tomatoes can be expected to weigh between 0.31 and 0.91 pound?

11. Answer to #4

12. Homework  13.5 worksheet