1. Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months. What is the probability of having one or less collision over a four-month period? Round you answer to 3 decimal places.

2. The U.S. national average door-to-doctor wait time for patients to see a doctor is now 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much shorter than the mean to see the doctor. Based on this information, 10% of patients will have to wait less than how many minutes to see a doctor? Round your answer in one decimal place.

3. A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. Suppose a random sample of 20 American workers is selected. Based on the relevant binomial distribution, answer the following questions about X, the number of American workers who say job stress caused frequent health problems:

What is the probability that X is no more than 12? Round your answer to 3 decimal places.

4. A survey conducted for theNorthwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. Suppose a random sample of 20 American workers is selected. Based on the relevant binomial distribution, answer the following questions aboutX, the number of American workers who say job stress caused frequent health problems:

What is the probability that X is at least 15? Round your answer to 3 decimal places.

5. According to CBS Money Watch, the average monthly household cellular phone bill is $100. Suppose monthly household cell phone bills are normally distributed with a standard deviation of $11.35. What is the probability that a randomly selected monthly cell phone bill is more than $120? Round your answer to 3 decimal places.

6. According to CBS Money Watch, the average monthly household cellular phone bill is $100. Suppose monthly household cell phone bills are normally distributed with a standard deviation of $11.35. What is the probability that a randomly selected monthly cell phone bill is between $80 and $110? Round your answer to 3 decimal places.

7. Consider a random variable with the following probability distribution:

X P(X)

0 0.25

1 0.5

2 0.25

What is the expected value (mean) of X?

8. Suppose that a marketing research firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with probability 0.40. What is the probability thatbothquestionnaires are returned? Round your answer to 2 decimal places.

9. If A and B are any two events with P(A) = .3 and P(B|A) = .5, then the joint probability of A and B is?