Question: The Army gives a battery of exams to all new recruits. One exam measures a person’s ability to work with technical machinery. This exam was given to a random sample of 360 new recruits. In the table below x = score on the test and f is the frequency of new recruits with score x.

a. Find the probability distribution for these scores.

b. Draw a histogram of the probability distribution.

c. The ground-to-air missile battalion needs people with a score of 7 or higher on the exam. What is the probability that a new recruit will meet this criterion?

d. The kitchen battalion can use people with scores of three or less. What is the probability that a new recruit is not overqualified for this work?

e. Compute the expected value of these scores.

f. Compute the standard deviation of these scores.