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the regression line

4.      Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?A. 2                        B. 4                            C. 3                             D. 5

                        E(2) = np = 32(1/8) = 4

5.      A class consists of 50 women and 82 men. If a student is randomly selected, what is the probability that the student is a woman?

A. 32/132 B. 25/66C. 50/132          D. 82/132

            P(woman) = 50 / (50 + 82) = 50/132 = 25/66

6.      If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that at least two heads occur consecutively?

A. 1/8          B. 3/8           C. 5/8       D. 6/8

            P(two consecutive H) = (Number of combinations with HH) / (Total number of                                                                  combinations)

            P(two consecutive H) = 3/8

7.      Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?

A. $0.00       B. −$0.40       C. −$1.00        D. −$0.50

            E(x) = (1/1000)($500) – 1 = $0.50 – $1 = -$0.50

8.      If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails?

A. 1/2        B. 2/3           C. 3/4        D. 4/9

            P(at least 2 T) = (Number of combinations with 2 or more T) / (Total number

                                                of combinations)

            P(at least 2 T) = 4/8 = ½