Question

In the last election, a state representative received 20 % 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 19% of the sample would vote for him? (Find the nearest answer) For the simplicity of algebra, use the following approximations if needed: V0.2 0.45,V.8 0.89, and 0.16 0.4 a.59.871% b. 95.994% C. 98.778% d. 77.337% e89.435% QUESTION 2 The amount of time an investment banker devotes to his/her job per week is normally distributed with a mean of 70 hours and a standard deviation of 6 hours Find the probability that the mean amount of work per week for 9 randomly selected investment bankers is more than 72 hours. (Find the nearest answer.) a. 0.2275 0.22663 0.06681 d. 0.15866 e.0.11507

Answer 1

From the given information,

Question 1

Using binomial probability calculater and normal approximation,

The required probability is

P(X>19)=59.871%

Hence, option a is correct.

Question 2

Here,

Z-value=(72-70)/(6/sqrt(9))

Z-value=1

So using standard normal probability table,

P(X>72)=0.15866

Hence, option d is correct.

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