Name ______
AP STATISTICS CHAPTER 7
Define each term and give an example:
Random Variable -
Discrete Random Variable -
Continuous Random Variable -
Probability Distribution:
The probabilities must satisfy two requirements:
1.
2.
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
Ex: Two dice are tossed. Consider the sum of their faces
Value of X:23456789101112
Probability:
PROBABILITY HISTOGRAM:
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
A CONTINUOUS RANDOM VARIABLE X takes on all in an of numbers.
THE PROBABILITY DISTRIBUTION of X is described by a .
Recall: the area under a is .
Ex:
distributions are distributions.
If X has the distribution, then the standardized variable is a standard normal variable having the distribution .
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
Consider the following game of chance played in a casino. You place $100 on the table, and win the amount the spinner points to after it is spun.
Perform an experiment to play the game 50 times. Record the results on a separate piece of paper.
What was your average dollar amount spun?
What was the standard deviation of your spins?
To find the mean of X, , then
=
is also called the
In the spinner example:
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
The law of large numbers says…..
Given that mu is the mean of X, the variance of X is given by,
The standard deviation of X is the square root of the variance.
RULES FOR MEANS
RULES FOR VARIANCES
If X and Y are independent, then…
If X and Y are dependent, we must consider their .
Examples:
Tom and George are playing in the club golf tournament. Their scores vary as they play the course repeatedly. Tom’s scores X has the N(110,10) distribution, and George’s score Y varies from round to round according to the N(100,8) distribution.
1. What is the mean of the difference between their scores?
2. What is the standard deviation of the difference between their scores?
3. If they play independently, what is the probability that Tom will score lower than George and thus do better in the tournament?
Sharonda and Lizette have been playing basketball for neighboring schools since they were freshmen phenoms. Now seniors, the media has been calling them “the two best female players in the district”. Friends want to know which player has the better record. The career average number of points scored by Sharonda is 17.3 with standard deviation 4.2. Lizette’s career average number of points has mean 18.9 with standard deviation 7.5.
1. Find the mean of the difference between Sharonda’s and Lizette’s career average number of points scored per game.
2. Suppose the official in your district who is responsible for sports statistics feels that the performances of the girls on the court can be considered independent. With this assumption, find the standard deviation of the difference between their current average number of points scored per game.
3. Now suppose that you disagree with the official and feel that the intensity of their rivalry strongly suggests that their performances on the court are not independent. You are comfortable assigning correlation p = 0.1 between their average point productions. Find the standard deviation of the difference in their average number of points scored using this assumption.
SUMMARY/QUESTIONS TO ASK IN CLASS
Name ______
AP STATISTICS CHAPTER 7
EXPECTED VALUE PROBLEMS
A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.
1.What is the probability that no customers make a purchase during the first hour that the store is open?
2.What is the probability that the number of customers that make a purchase during the first hour that the store is open is more than 1 but no greater than 3?
3.Find the mean number of customers that make a purchase during the first hour that the store is open.
4.Find the standard deviation of the number of customers that make a purchase during the first hour that the store is open.
5.Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X is normal with a mean of $360 and standard deviation $50. The probability is approximately 0.6 that on a randomly selected day the store will make less than x0 amount of profit. Find x0.
The probabilities that a customer selects 1, 2, 3, 4, or 5 items at a convenience store are 0.32, 0.12, 0.23, 0.18, and 0.15, respectively.
6.Construct a probability distribution (table) for the data, and verify that this is a legitimate probability distribution.
7.Find the mean of the random variable, X.
8.Find the standard deviation of X.
9.Here’s a game: If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If the person gets a 7, he wins $5. The cost to play the game is $3. Find the expected payout for the game.
SUMMARY/QUESTIONS TO ASK IN CLASS