Question

1.   Dr. Cornie developed a test to measure Boredom. He administered it to a group of 20,000 adults. The possible scores were 1, 2, 3, 4, 5, 6, and 7 with 7 indicating the highest tolerance for boredom. The results are shown. Complete the following table and then find the mean, variance, and standard deviation to measure boredom tolerance of the adults.

Score X

1

2

3

4

5

6

7

Frequency f

1400

2600

3600

6000

4400

1600

400

Probability P(X)

 

 

 

 

 

 

 

Answer 1

Solution:

Now, mean$=\Sigma X.P(X)=3.79$

And variance$=E(X^2)-[E(X)]^2=16.37-(3.79)^2=2.0059$

Then, standard deviation$=\sqrt{2.0059}=1.416$