In the last election, a state representative received 40% of the votes cast. One

Question

In the last election, a state representative received 40% of the votes cast. One year after the election, the representative organized a survey that asked a random sample of 100 people whether they would vote for him in the next election. If we assume that his popularity has not changed, what is the probability that more than half of the sample would vote for him? (Find the nearest answer.) For the simplicity of algebra, use the following approximations if needed: squareroot0.2 0.45, squareroot0.24 0.49, and squareroot0.4 0.63 a. 4.457% b. 3.593% c. 8.076% d. 2.068% e. 6.681%

Explanation / Answer

Compute 1-proportion Z test to find the probability of more than half of the sample to vote the representative.

Z=(Ps-Pu)/sqrt [Pu(1-Pu)/N], Where, Ps is sample proportion, Pu is population proportion an N is sample size.

Z=(0.40-0.50)/sqrt [0.5(1-0.5)/100]

=-2.

P(Z>-2)=0.02275

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