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)

Find Mean & Standard Deviation: x = # books read P(x)

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)

LINEAR TRANSFORMATIONS Section 6.2A

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

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

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

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

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

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?

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

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

Variance of y = a + bx Relates to slope.

*Shape remains the same.

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

Mean of the Sum of Random Variables

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

Variance of the Sum of Random Variables

Meanst dev x205 y243

Meanst dev x205 y243

Meanst dev x205 y243

Meanst dev x205 y243

Find: and xP(x)yP(y)

Homework Worksheet