Answer to Question #189757 in Statistics and Probability for Jon jay Mendoza

Question

2. 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 Frequency f

1 1400

2 2600

3 3600

4 6000

5 4400

6 1600

7 400

Probability P(X)

 

 

 

Answer 1

Table :

So, from the table

Mean $=\sum X\cdot P(X)=3.79$

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

Standard Deviation $=\sqrt{Variance}=\sqrt{{2.0059}}=1.416$

$P(X_1)=\dfrac{1400}{20,000}=0.07\\P(X_2)=\dfrac{2600}{20,000}=0.13\\P(X_3)=\dfrac{3600}{20,000}=0.18\\P(X_4)=\dfrac{6000}{20,000}=0.30\\P(X_5)=\dfrac{4400}{20,000}=0.22\\P(X_6)=\dfrac{1600}{20,000}=0.08\\ \\P(X_7)=\dfrac{400}{20,000}=0.02$