1. A sample of 150 people are checked to determine their blood type. The results show that 60 have type O, 40 have Type A, 30 have type B and the remaining individuals have Type AB. If one person is randomly selected, what is the probability that this person has either type A or type AB blood?
2. At a party of 10 men and 20 women, four of the men and 10 of the women are smokers. If two men and two women are randomly selected, approximately what is the probability that all four are smokers?
3. On a charter flight, the mean weight of all the children aboard the plane is 70 pounds, and their total weight is 1050 pounds. The mean weight of all men is 160 lbs., and their total weight is 1920 lbs. The 18 women on the flight have a total weight of 2070 lbs. What is the mean weight of all the people on this flight?
4. A woman has three pair of stockings similar in color. If she decides to pair the six stockings in a random fashion, what is the probability that each stocking has been properly matched?
5. A population of data consists only of the numbers 4, 6, 8, 10, and 12. There are seven 4's, four 6's, and eight 8's. If this population's modes are 8 and 10, what is the maximum allowable number of data?
6. In a normal distribution of data, the mean is 30, and the standard deviation is 4. Among the following, which raw score has the lowest frequency?
7. In a standardized normal distribution, the mean= _____ and the standard deviation = _______
8. An extremely large population has a mean of 16 and a standard deviation of 8. Consider all possible samples of size 100. What would be the value of the standard deviation of the 100 sample means?
9. Lamps used to light streets have a mean lifetime of 350 days and a standard deviation of 30 days. Assuming that the lifetimes of these lamps represent a normal distribution and a continuous random variable, approximately what percent of these lamps will last less than 305 days?
10. An aptitude test was given to 150 applicants, and the resulting scores were put into grouped data form. The first interval consisted of scores ranging from 10 through 19; the second interval contained scores of 20 through 29, etc. The last interval contained scores of 90 through 99. If 47 scores are less than 50, and 42 scores lie in the interval with scores from 50 through 59, what is the best estimate of the median score?
11. In a group of 32 car batteries, the lifetimes are found to have a mean of four years and a standard deviation of 1.5 years, using Chebyshev's Theorem. What is the maximum number of batteries which will last longer than 10 years?
12. Given a normal distribution (of continuous data) in which the mean is 150 and the standard deviation is 12, which score separates the lower 4% from the upper 96%?
13. A sample of six data is arranged in ascending order. The lowest value is 8 and the range of the data is 10. Which one of the following statements must be true?
14. In your first course at Cal Tech, the prof bases the course grade on one quiz, one mid-term, and one final. The quiz counts 20% and the midterm counts 35%. If your quiz was 90% and your midterm was only 70%, what is the minimum grade you need to score on the final to get an 80% in the class?
15. There are two finalists in a golf tournament, with the winner getting $40,000 and the runner-up getting $15,000. If the mathematical expectation of the better player is $32,000, what is his probability of winning?
16. Given a binomial distribution in which the probability of success is .88 and the number of trials is 20, what is the approximate probability of getting at least 19 successes?
17. A doctor knows 15% of all her patients are late for their appointments. Given five randomly selected patients, what is the approximate probability that exactly three of them are late for their appointments?
18. Given events A,B where P(A) = .25, P(B) = .3. If P(A|B)=.40 what is the P(B|A)?
19. Using the Poisson distribution and assuming a bank averages seven bad checks a day, what is the approximate probability that the bank receives 5 bad checks on a given day?
20. In a certain frequency table of grouped data, the class marks for the first three classes are 7.5, 8.2, 8.9, respectively. Assuming all classes have the same width and given that the lower limit for the first class is 7.2, what is the lower boundary for the third class? (Hint: lower boundary is not the same as lower limit)
21. In a music class of five students, each listens to the same four songs. Each student then his or her favorite song without consulting the other students. What is the approximate probability that all five students select the same song?
22. Given any two positive standardized z-scores of a standard normal distribution, which of the following statements must be true?
23. For which of the following samples is the coefficient of variation the smallest? (Hint: The coefficient of variation is 100*s/)
24. Given events A, B are independent and P(A) = 1/3, which of the following conditions could exist?
25. A license plate consists of two letters followed by three odd integers. A letter may be repeated, but the three digits must be different. How many different license plates are there?
26. Given an extremely large size for a population, suppose a sample of this population has 144 data, with a mean of 18 and a standard deviation of 6. With what percent confidence (approximately) can it be stated that the actual mean of the population lies between 17.5 and 18.5?
27. If a distribution of data has no mode, which of the following conditions must exist?
28. A delivery company has 20 trucks, three of which have faulty brakes. If three of the 20 trucks are randomly selected, what is the approximate probability that the first two trucks have good brakes, and the third truck has faulty brakes?
29. In a sample of data, the 20th percentile is 30, the 50th percentile is 40, the 70th percentile is 48, and the mean is 35. Which of the following would convert to a positive z-score and have an original value lower than the median?
30. Next weekend, you are expecting a visit from doting relatives. The probability that Aunt Merna will show up is .4, whereas the probability that Uncle Wilbur will show up is .8. What is the probability that at least one of them will visit you next weekend?
31. There is a dinner party in Pleasantville where five couples get together. If each wife gives a gift to everyone at the party except herself and her own husband, how many gifts are given?
32. Assuming an ordinary, fair, six-sided die, what are the approximate odds against getting a "2" twice when tossing this die nine times?
33. How many different ways can you arrange the all the letters of the word "INDIVIDUAL"?
34. In a sample of five pieces of data, the standard z-scores for three of the data are -1.1, -0.3, and 0.2. If the remaining two pieces of data have the same z scores, what is the value of the z-scores?
35. A distribution of data is positively skewed. This implies which of the following?