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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

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

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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

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

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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?

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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?

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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 players average gain?

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LINEAR TRANSFORMATIONS Section 6.2A

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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

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Adding/Subtracting a constant from data shifts the mean but doesnt change the variance or standard deviation.

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

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Petes 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

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Petes 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

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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?

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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 dealerships 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

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Suppose the dealerships 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

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Variance of y = a + bx Relates to slope.

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*Shape remains the same.

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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. Whats the mean number of cars entering the freeway. Road Mean # Cars 1800 21000 3600

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Mean of the Sum of Random Variables

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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

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Variance of the Sum of Random Variables

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Meanst dev x205 y243

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Meanst dev x205 y243

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Meanst dev x205 y243

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Meanst dev x205 y243

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

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Homework Worksheet

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