1. Warm Up How do I know this is a probability distribution? What is the probability that Mary hits exactly 3 red lights? What is the probability that she gets at least 4 red lights? What is the probability that she gets less than two? Find the mean & standard deviation. x=# red lightsp(x) 00.05 10.25 20.35 30.15 4 50.05

2. Find Mean & Standard Deviation: x = # books read P(x) 00.13 10.21 20.28 30.31 40.07

3. Ex. 1. Find the mean 2. Find the Standard Deviation 3. Find the probability that x is within one deviation from the mean. x = possible winnings P(x) 50.1 70.31 80.24 100.16 140.19

4. LINEAR TRANSFORMATIONS Section 6.2A

5. Remember – effects of Linear Transformations Adding or Subtracting a Constant Adds “a” to measures of center and location Does not change shape or measures of spread Multiplying or Dividing by a Constant Multiplies or divides measures of center and location by “b” Multiplies or divides measures of spread by |b| Does not change shape of distribution

6. Adding/Subtracting a constant from data shifts the mean but doesn’t change the variance or standard deviation.

7. Multiplying/Dividing by a constant multiplies the mean and the standard deviation.

8. Pete’s Jeep Tours offers a popular half-day trip in a tourist area. The vehicle will hold up to 6 passengers. The number of passengers X on a randomly selected day has the following probability distribution. He charges $150 per passenger. How much on average does Pete earn from the half-day trip? # PassengersProb 20.15 30.25 40.35 50.2 60.05

9. Pete’s Jeep Tours offers a popular half-day trip in a tourist area. The vehicle will hold up to 6 passengers. The number of passengers X on a randomly selected day has the following probability distribution. He charges $150 per passenger. What is the typical deviation in the amount that Pete makes? # PassengersProb 20.15 30.25 40.35 50.2 60.05

10. What if it costs Pete $100 to buy permits, gas, and a ferry pass for each half-day trip. The amount of profit V that Pete makes from the trip is the total amount of money C that he collects from the passengers minus $100. That is V = C – 100. So, what is the average profit that Pete makes? What is the standard deviation in profits?

11. A large auto dealership keeps track of sales made during each hour of the day. Let X = the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of X is shown below. Suppose the dealership’s manager receives a $500 bonus from the company for each car sold. What is the mean and standard deviation of the amount that the manager earns on average? # cars soldProb 00.3 10.4 20.2 30.1

12. Suppose the dealership’s manager receives a $500 bonus from the company for each car sold. To encourage customers to buy cars on Friday mornings, the manager spends $75 to provide coffee and doughnuts. Find the mean and standard deviation of the profit the manager makes. # cars soldProb 00.3 10.4 20.2 30.1

13. Variance of y = a + bx Relates to slope.

14. *Shape remains the same.

15. Example: Three different roads feed into a freeway entrance. The number of cars coming from each road onto the freeway is a random variable with mean values as follows. What’s the mean number of cars entering the freeway. Road Mean # Cars 1800 21000 3600

16. Mean of the Sum of Random Variables

17. Ex: What is the standard deviation of the # of cars coming from each road onto the freeway. Road Mean # Cars St. Dev. 180034.5 2100042.8 360019.3

18. Variance of the Sum of Random Variables

19. Meanst dev x205 y243

20. Meanst dev x205 y243

21. Meanst dev x205 y243

22. Meanst dev x205 y243

23. Find: and xP(x)yP(y) 30.32100.22 40.14200.34 50.12300.18 60.42400.26

24. Homework Worksheet