1 In the last election a state representative received 40 of

1) 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:

a.3.593%

b.6.681%

c.2.068%

d.4.457%

e.8.076%

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 5 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.)

0.06681

0.2275

0.11507

0.15866

0.22663

3) The probability distribution of job satisfaction scores for senior executives are as follows.

Job Satisfaction

1

2

3

4

5

probability

0%

10%

20%

30%

40%

If you survey 100 senior executives, what is the probability that the average job satisfaction score is lower than 3.8?

0.97725

0.02275

0.15866

0.5

0.84134

Solution

1.

We first get the z score for the critical value:          
          
x = critical value =    50      
u = mean = np =    40      
          
s = standard deviation = sqrt(np(1-p)) =    4.898979486      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    2.041241452      
          
Thus, the left tailed area is          
          
P(z <   2.041241452   ) =    0.020613417 approx 2.068% [ANSWER, OPTION C (closest)]