Three businesswomen are trying to convene in Cincinnati for a business meeting. The first women (Woman 1) is arriving on a flight from Atlanta, the second (Woman 2) is arriving on a flight from Dallas, and the third (Woman 3) is arriving on a flight from Chicago. Historical data suggests that the Atlanta flight is “on time” 90% of the time, the Dallas flight is “on time” 95% of the time, and the Chicago flight is “on time” 80% of the time. Furthermore, historical data suggests that the three flights are independent with respect to on time behavior.

1. Define the sample space for this random experiment.
2. Compute the probability for each of the outcomes in the sample space.

Let  W denote the number of business women that arrive on time.

1. Construct the probability mass function of W
2. Construct the cumulative distribution function of W
3. Find the expected value of W
4. Compute the standard deviation of W