Review Questions for Probability

(chapter 6) If it rains while you are driving, you have a 0.5 percent chance (.005) of getting into an accident. It rains 5 percent (.05) of the time. Overall, you get in accidents .3 percent (.003) of the time. If you get into an accident, what is the probability that it was raining? Is rain positively related, negatively related, or uncorrelated with accidents?

(chapter 7) The average age of first marriage for men is 25.3 years with a standard deviation of 4.6 years. The average of first marriage for women is 23.7 years with a standard deviation of 4.4 years. You are interested in the mean and standard deviation of the difference in ages of men and women when they get married. What does it mean to assume independence in this case? Is independence a reasonable assumption? Do you need to assume independence to calculate the mean difference? The standard deviation of the difference? Calculate both, using whatever assumptions you need.

(chapter 8) Sketch-e Airlines has an average on-time performance of 52 percent. What is the probability that in 10 flights they will have exactly 7 planes arrive on time? What is the probability that they will have more than 6 planes arrive on time?

(chapter 2) Slez-e Airlines has an average arrival time of 8.5 minutes late, with a standard deviation of 10 minutes. What is the probability that for the next flight the average arrival time will be 0 minutes late or less?

(chapter 9) What is the Central Limit Theorem, and why is it significant?