The United States Coast Guard (USCG) provides a wide variety of information on boating accidents including the wind condition at the time of the accident. The following table shows the results obtained for 4401 accidents (USCG website, November 8, 2012).

Percentage of

Wind Condition Accidents

None ............ 9.6

Light ............57.0

Moderate ..........23.8

Strong .......... 7.7

Storm .......... 1.9

Let x be a random variable reflecting the known wind condition at the time of each accident. Set x = 0 for none, x = 1 for light, x = 2 for moderate, x = 3 for strong, and x = 4 for storm.

a. Develop a probability distribution for x.

b. Compute the expected value of x.

c. Compute the variance and standard deviation for x.

d. Comment on what your results imply about the wind conditions during boating accidents.