Question: An industrial psychologist administered a personality inventory test for passive-aggressive traits to 150 employees. Individuals were rated on a scale from 1 to 5, where I was extremely passive and 5 was extremely aggressive. A score of 3 indicated neither trait. The results are shown below.

Score, x Frequency P(X = x)

1 24

2 33

3 42

4 30

5 21

a) Create a probability distribution for the random variable X, the score of the personality test by filling in the last column of the table above.

b) Draw the probability histogram.

c) Compute and interpret the mean of the random variable x.

d) Compute the variance and standard deviation of the random variable x.

e) What is the probability that a score of 3 of less is obtained?