ONLY QUESTION #2

1. Think of the situation of rolling two dice. Let M denote the sum of the number of dots on the two dice. (Hence, at any trial, M is a number between 2 to 12.) a. In a table, list all the possible outcomes for the random variable M together with its probability distribution and cumulative probability distribution. Sketch both distributions. (3 Marks) b. Calculate the expected value and the standard deviation for M. (4 Marks) c. Looking at the sketch of the probability distribution, you notice that it resembles a normal distribution. Should you be able to use the standard normal distribution to calculate probabilities of events? Why or why not? Explain. (3 Marks)

Results of # 1

Var(M) = P(M) x (M-Mm)^2 = 5.833

E(M)= 7

SD= 5.833= 2.415

2. By looking at the results of activity #1 above, what is the probability (show it in percentage) of the following outcomes? (Show your calculations on each)

a. Pr(M = 8) (1 Mark)

b. Pr(M = 6) (1 Mark)

c. Pr(M = 4 or M = 12) (2 Marks)

d. Pr(M = 7 or M 7) (2 Marks)

e. Pr(M < 10) (2 Marks)

f. Pr(M = 7 or M > 11) (2 Marks)