The probability model describes the number of repair

The probability model describes the number of repair calls that an appliance repair shop may receive during an hour. a)How many calls should the shop expect per hour? b)What is the standard deviation? Repair Calls 0 1 2 3 Probability 0. 1 0. 3 0. 4 0. 2

A man buys a racehorse for $20, 000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $100, 000. If it wins one of the races, it will be worth $50, 000. If it loses both races, it will be worth only $10, 000. The man believes there’s a 20% chance that the horse will win the first race and a 30% chance it will win the second one. Assuming that the two races are independent events, find the man’s expected profit.

Chapter 16 Part 3 MORE ABOUT MEANS AND VARIANCES

Adding a constant to data (adding the same amount to each value) shifts the mean but the variance and standard deviation do not change.

Example: Couples at the Quiet Nook can expect discounts averaging $5. 83 with a standard deviation of $8. 62. Suppose that for several weeks the restaurant has also been distributing coupons worth $5 off any one meal per table. If every couple there brings a coupon, what will be the mean and standard deviation of the total discounts they’ll receive? E(x) = 5. 83 + 5 = $10. 83 SD(x) = $8. 62 (unchanged)

Multiplying each value of a random variable by a constant multiplies the mean and the standard deviation by that constant.

Example: (continued) Couples at the Quiet Nook can expect discounts averaging $5. 83 with a standard deviation of $8. 62. When two couples dine together on a single check, the restaurant doubles the discount offer - $40 for the ace of hearts on the 1 st draw or $20 for ace of hearts on 2 nd draw. What are the mean and standard deviation?

Example: Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: Standard Mean 2 Y + 20 Deviation Mean = E(2 Y+20) = 2 E(Y)+20 = 2(12)+20 = 44 X 80 12 SD = SD(2 Y+20) = 2 SD(Y) = 2(3) = 6 Y 12 3

Adding/Subtracting Random Variables: If X and Y are independent, then

Example: Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: Standard Mean X+Y Deviation X 80 12 Y 12 3

Mean Standard Deviation X 80 12 Y 12 3

Answers: a)240; 36 b)32; 4. 24 c)20; 19. 21 d)240; 20. 78

Today’s Assignment: q. Add to HW: p. 384 #24 -26, 33 -36 q. Chapter 16 HW Due Monday 12 -7 -15