Question

Problem #1

You ask your graduate student to roll a die 5000 times and record the results.

a)     Give the expected mean and standard deviation of the outcome.

P= 1/6 , Q= 5/6

NP= 5,000

NP X P= 5,000 *1/6 =

5,000/6

SD: Square root(5,000 * 1/6 * 5/6) = Square Root

b) The die roll experiment is repeated (though with a different graduate student – for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 11% of the time, a 1 shows up 21% of the time, and all remaining numbers show up 68% of the time (17% each). Now what is the expected mean and sd of 5000 rolls?

Problem #2

Part a: A product manager is evaluating production and inventory. In looking over the data, she decides that a product should be continued if it sold 23,000 over the previous year. In addition, the product is considered “popular” if it receives 50 mentions by the local press over the past year.

In selecting a product at random from the catalog, let C be the likelihood that this particular product sold 23,000 products the past year. Let P be the likelihood that the product received the 50 or more mentions by the local press.

The analyst determines that P(C) = 0.297, P(P) = 0.162, and the probability that a product has sold 8000 items, and was ‘popular’ is 0.083. What is the probability that a randomly selected product either sold the requisite 23,000 items, or that it is ‘popular’?

Part b: Where would the analyst have come up with the probaility values for P(C) andP(P)?

Problem #3

You are playing a game of backgammon, and realize that if either of the two dice on your next roll is a 4, you will win the game. (It’s also fine for both dice to be a 4, but you only need one). However, if you don’t get a 4 on either die, your opponent will win on their next move.

Just to restate: As long as you see a 4 on either of the dice, you will win, otherwise you lose. What is the probability that you will win the game?

Problem #4

You are a coach of a basketball team, and the final game of the season is on the line. Here are the current season’s data for your two best shooters, Lisa and Maggie. The {0, 1, 2, 3} represents the number of baskets they made out of the 3 throws. For example, Lisa makes all 3 baskets 10% of the time, and makes 0 (ie misses all 3) 16% of the time.

Lisa	0	1	2	3
Prob.	.16	.45	.29	.1

Maggie	0	1	2	3
Prob.	.17	.45	.25	.13

a)     You must pick one of the following two players to make 3 free-throw attempts. Which one is most likely to give you your best result? Be sure to explain why.

b)      Suppose you needed to make all 3 baskets in order to win, otherwise you would lose. Who would you pick? B

Answer 1

Problem 4 Answer:

Given Data

the final game of the season is on the line

The {0,1,2,3} represents the number of baskets they made out of the 3 throws.

X : Number of baskets made

a)

You must pick one of the following two players to make 3 free-throw attempts. Which one is most likely to give you your best result? Be sure to explain why.

Expected Number of baskets made by lisa : E(X) for lisa

= 0 x 0.16 + 1 x 0.45 + 2 x 0.29 + 3 x 0.1

= 0+0.45+0.58+ 0.3

= 1.33

Expected Number of baskets made by Maggie : E(X) for Ashley

= 0 x 0.17 + 1 x 0.45 + 2 x 0.25 + 3 x 0.13

= 0+0.45+0.5+0.39

= 1.34

Expected Number of baskets made by Maggie :1.34 > Expected Number of baskets made by Lisa:1.33

Maggieis most likely to give you your best results.

b) Suppose you needed to make all 3 baskets in order to win, otherwise you would lose. Who would you pick? Be sure to explain your thinking.

You would pick that person :who have the higher probability to make all 3 baskets

Maggie's probability to make all 3 baskets: 0.13 > Lisa : probability to make all 3 baskets: 0.09

You would pick Maggie