1. Warm-up The mean grade on a standardized test is 88 with a standard deviation of 3.4. If the test scores are normally distributed, what is the probability that a person scored less than an 84?

2. MEAN & STANDARD DEVIATION Section 6.1B

3. Warm-up The probability that a person fails the 9 th grade is 0.22. Let x = the number of people out of 3 who fail the 9 th grade. Write the probability distribution of x.

4. What about if there were 4 people?

5. Mean Value of Random Variable Describes where the probability distribution of x is centered. Symbol is Where do you think the mean is located on the problem we did as a warm-up?

6. Standard Deviation Describes the variation of the distribution. Symbol is If it’s small, then x is close to the mean. If it’s large then there’s more variability.

7. Flip 3 coins – what’s the mean number of heads. x = # heads p(x) 0 1 2 3

8. Formula It’s also known as the Expected value and is written E(x).

9. Apgar scores – 1 min. after birth and again 5 min. Possible values are from 0 to 10. Find the mean. x012345678910 P(x)0.0020.0010.0020.0050.020.040.170.380.250.120.01

10. What about the standard deviation? How do you think we find it?

11. Variance : Standard Deviation:

12. Apgar scores – Calculate the standard deviation x012345678910 P(x)0.0020.0010.0020.0050.020.040.170.380.250.120.01

13. Find Mean & Standard Deviation: x = # cars at red light P(x) 00.13 10.21 20.28 30.31 40.07

14. 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

15. 500 raffle tickets are sold at $2 each. You bought 5 tickets. What’s your expected winning if the prize is a $200 tv.?

16. 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?

17. 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?

18. 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?

19. Homework Page 354 (9 – 12),15, 16, 18, 19, 28, 29, 30)