In general, it is better to also show the numbers and methodology you used to calculate the answer, step by step, instead of simply showing the calculated value. Provide as many intermediate reducing calculations as you think are needed to clearly indicate what you were trying to do. That way, you may still receive partial credit even if your answer is incorrect because your methodology was correct

1. Find the mean, variance, and standard deviation for the distribution.

2. Compute the probability of X successes, using Table B in Appendix A.

3. Compute the probability of X successes, using the binomial formula.

4. A survey found that 10% of Americans believe that they have seen a UFO. Assume a sample of 10 people. Look up the values from Binomial Distribution Table B in Appendix A.

5. Find the mean, variance, and standard deviation for the number of heads when 10 coins are tossed. Assume a binomial distribution.

6. A survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 16 pet owners are randomly selected, find the probability that exactly 5 people have their pets bathed professionally. Assume a binomial distribution from Table B.

7. If 4% of all cars fail the emissions inspection, find the probability that in a sample of 100 cars, 3 will fail. Use the Poisson approximation from Table C.

8. Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD. Assume a hypergeometric distribution.

9. Using the multinomial formula and find the probability where

n = 6, X1 = 3, X2 = 2, X3 = 1, p1 = 0.5, p2 = 0.3, p3 = 0.2.

10. A person calls people to ask if they would like to extend their automobile insurance beyond the normal 3 years. The probability that the respondent says yes is about 33%. If she calls 12 people, find the probability that the first person to say yes will occur with the fourth customer.