QUESTION 1 A state senator believes that 30% of all senators on the Finance Comm

Question

QUESTION 1 A state senator believes that 30% of all senators on the Finance Committee will strongly support the tax proposal she wishes to advance. Suppose that her belief is correct and that 5 senators are approached at random. What is the probability that at least 2 senators will strongly support the proposal? (Round the answer to the second decimal place.)

a. 81.25%

b. 91.30%

c. 26.27%

d. 47.18%

e. 66.30%

QUESTION 2

An official from the securities commission estimates that 80% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry. Find the probability that 12 or fewer online bankers have profited from insider information. (Find the nearest answer.

60.20%

97.29%

18.41%

87.32%

76.39%

60.20%

97.29%

18.41%

87.32%

76.39%

Explanation / Answer

1.

x = number of successes

Probability of x successes = nCx x px  x (1-p)n-x

probability that a senator would strongly support = 0.3

Probability (x > = 2) = 5C2 x 0.32 x 0.73 + 5C3 x 0.33 x 0.72 + 5C4 x 0.34 x 0.71 + + 5C5 x 0.35 x 0.70

Probability (x > = 2) = 0.4718 (Option d is correct)

2.

x = number of successes

probability that online bankers have profited = 0.8

Probability (x < = 12) = 1 - (15C13 x 0.813 x 0.22 + 15C14 x 0.814 x 0.2+ 15C15 x 0.815 x 0.20)

(= 1 - P(13 successes) - P (14 successes) - P (15 successes))

Probability (x < = 12) = 0.602 (Option a is correct)

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