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Warm Up

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.

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Warm Up

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  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.

  2. Find Mean & Standard Deviation:

  3. Ex. • Find the mean • Find the Standard Deviation • Find the probability that x is within one deviation from the mean.

  4. 500 raffle tickets are sold at $2 each. You bought 5 tickets. What’s your expected winning if the prize is a $200 tv.?

  5. There are four envelopes in a box. One envelope contains a $1 bill, one contains a $5, one contains a $10, and one a $50 bill. A person selects an envelope. Find the expected value of the draw. What should we charge for the game for it to be fair?

  6. A person selects a card from a deck. If it is a red card, he wins $1. If it is a black card between or including 2 and 10, he wins $5. If it is a black face card, he wins $10, and if it is a black ace, he wins $100. Find the expectation of the game. What would it be if it cost $10 to play? What should I charge to make it a fair game?

  7. On a roulette wheel, there are 38 slots numbered 1 through 36 plus 0 and 00. Half of the slots from 1 to 36 are red; the other half are black. Both the 0 and 00 slots are green. Suppose that a player places a simple $1 bet on red. If the ball lands in a red slot, the player gets the original dollar back, plus an additional dollar for winning the bet. If the ball lands in a different-colored slot, the player loses the dollar bet to the casino. What is the player’s average gain?

  8. Linear Transformations Section 6.2A

  9. 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

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

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

  12. 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?

  13. 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?

  14. 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?

  15. 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?

  16. 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.

  17. Variance of y = a + bx • Relates to slope.

  18. Effects of Linear Transformation on the Mean and Standard Deviation if . = *Shape remains the same.

  19. 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.

  20. Mean of the Sum of Random Variables For any two random variables, X and Y, if then the expected value of T is +

  21. Ex: What is the standard deviation of the # of cars coming from each road onto the freeway.

  22. Variance of the Sum of Random Variables For any two random variables, X and Y, if then the variance of T is

  23. Find: and

  24. Homework Worksheet

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