Download rs3 exercises - Graduate Institute of International and

Exercises Problem 1 The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour: Repair calls 0 1 2 3 P(x) 0.1 0.3 0.4 0.2 The probability that the number of repair calls is at least 2 is: (a) 0.8 (b) 0.2 (c) 0.4 (d) 0.6 Problem 2 In a litter of seven kittens, three are female. You pick two kittens at random. The probability model for the number of male kittens is: Number males 0 Probability 1 2 0.143 0.571 0.286 The expected number of males is: (a) 0.64 (b) 1.7 (c) 1.14 (d) 2.1 Problem 3 Let X represent a discrete random variable that takes any of the values and probabilities given below: X -­‐2 5 6 P(X) 0.4 0.4 __ The probability for X = 6 is missing. What is it? (a) It cannot be determined from the information given (b) 0.2 (c) 0.6 (d) 2.3 1 Problem 4 The manager of a stock room in a factory knows from her study of records that the daily demand for a certain tool has the following probability model: Demand 0 1 2 Probability 0.1 0.5 0.4 Suppose it costs the factory $10 each time the tool is used. Find the variance of the daily cost of using the tool. (a) 13 (b) 41 (c) 1.3 (d) 10 Problem 5 Which of the following would make the sampling distribution of the sample mean narrower? Check all answers that apply. (a) A smaller population standard deviation (b) A smaller sample size (c) A larger standard error (d) A larger sample size (e) A larger population standard deviation Problem 6 All other things being equal, as the sample size increases, the standard error of a statistic (a) Approaches the population mean in numerical value. (b) Approaches the standard deviation of the population. (c) Increases. (d) Remains constant if the value of sigma is known. (e) Decreases. Problem 7 Suppose that the distribution of X in the population is strongly skewed to the left. If you took 200 independent and random samples of size 3 from this population, calculated the mean for each of the 200 samples, and drew the distribution of the sample means, what would the sampling distribution of the means look like? (a) It will be perfectly normal and the mean will be equal to the median. (b) It will be close to the normal and the mean will be close to the median. (c) On a p-­‐plot, most of the points will be on the line. (d) It will be skewed to the left and the mean will be less than the median. 2 Problem 8 If you take all samples of a particular size from a particular population, find the mean of each sample, and then plot the distribution of the means, what have you created? (a) Sample distribution. (b) Sampling distribution. (c) Population distribution. Problem 9 The LAPD has been testing a new system of catching speeders on the 405 over the last 10 months. They wanted to see if they really were catching more speeders, so each month they took 20 samples (with replacement) from the tickets issued in this program . Because their sample sizes were always one-­‐fifth of the tickets, they increased in size each month. How did the sampling distribution of the mean change over the 10 months? (a) It became just one point -­‐ the true population mean (b) It became wider because they had more information (c) It became skewed to the right because very few people get more than 1 or 2 speeding tickets a year (d) It became more like the true distribution of the population of tickets issued (e) It became close to the normal distribution with the mean equal to the population mean Problem 10 The amount of money, college students spend each semester on textbooks is normally distributed with a mean of $195 and a standard deviation of $20. Suppose you take a random sample of 100 college students from this population. There is a 68% chance that the sample mean amount spent on textbooks is between: (a) $193 and $197. (b) $155 and $235. (c) $191 and $199. (d) $175 and $215. Problem 11 The weights of packets of cookies produced by a certain manufacturer have a normal distribution with a mean of 202 grams and a standard deviation of 3 grams. What is the weight that should be stamped on the packet so that only 0.99% of packets are underweight? (a) 200 (b) 195 (c) 190 (d) 205 3 Problem 12 GSP Inc. is trying two different marketing techniques for its toothpaste. In 20 test cities, it is using family branding. This sells toothpaste with a mean of 2,250 units per week and a standard deviation of 250 units per week. In 20 other test cities, GSP is using individual branding. This sells toothpaste with a mean of 2,250 units per week and a standard deviation of 500 units per week. GSP wants to select the marketing technique that sells at least 2,350 units per week more often. If the number of units sold per week follows a normal distribution, which marketing technique should GSP choose? (a) Individual Branding (b) Can't be answered with the information given (c) Family Branding (d) They each get the same result Problem 13 Among first year students at a certain university, scores on the verbal SAT follow the normal curve. The average is around 500 and the SD is about 100. Tatiana took the SAT, and placed at the 85% percentile. What was her verbal SAT score? (a) 604 (b) 560 (c) 90 (d) 403 Problem 14 A set of test scores are normally distributed. The mean is 100 and the standard deviation is 20. These scores are converted to z-­‐scores. What are the z-­‐scores of the mean and median? (a) 1 (b) 100 (c) 0 (d) 50 Problem 15 In Japan there is an annual turkey dog eating contest. The number of turkey dogs that contestants eat are normally distributed with a mean of 36 turkey dogs and a standard deviation of 6 turkey dogs. A contestant eats 27 turkey dogs. What is his z-­‐score? (a) 6 (b) -­‐1.5 (c) 9 (d) 1.5 (e) -­‐9
Problem 16 Years ago, the value of HBA1c, a test used to measure blood sugar level, was normally distributed with mean 6 and standard deviation 1. A diabetic person is anyone whose HBA1c is larger than 7. We want to find out (a) If I choose a person at random from the population, what is the probability that this person is NOT a diabetic? (b) If I take a random sample of 5 people what is the probability that their average HBAic is smaller than 7? (a) (a) approximately 0.9772 (b) approximately 0.0228 (b) (a) approximately 0.8413 (b) approximately 1 (c) None of the above (d) (a) approximately 0.8413 (b) approximately 0.9871 4 Problem 17 Given that the IQ scores in the population follow the normal distribution with mean (μ) equal to 100 and standard deviation (σ) equal to 15, what is the best answer? (a) If you pick a person at random, the chance that his IQ falls between 115-­‐130 is more than the chance that his IQ falls between 60-­‐85. (b) If you pick a person at random, the chance that his IQ falls between 115-­‐130 is equal to the chance that his IQ falls between 60-­‐85. (c) If you pick a person at random, the chance that his IQ falls between 115-­‐130 is not comparable to his IQ falling between 60-­‐85. (d) If you pick a person at random, the chance that his IQ falls between 115-­‐130 is less than the chance that his IQ falls between 60-­‐85. Problem 18 Scott's percentile rank in the verbal section of the SAT was 80. What can be assumed about his score? (a) Scott got 80% of the questions right (b) 80% of the students that took the test received a lower score than Scott (c) 80% of the students that took the test scored higher than Scott did (d) Scott answered at least 80% of the questions correctly Problem 19 In an article in the Journal of American Pediatric Health researchers claim that the weights of healthy babies born in the United States form a distribution that is nearly normal with an average weight of 7.25 pounds and standard deviation of 1.75 pounds. The US Department of Health classifies a newborn as "low birth weight" if her/his weight is less than 5.5 pounds. What is the probability that a baby, chosen at random, weighs less than 5.5 pounds? (a) About 16% (b) About 84% (c) About 90% (d) the probability cannot be determined (e) About 10% Source: UCLA webpage 5 Answers: 1. (d) 2. (c) 3. (b) 4. (b) 5. (a), (d) 6. (e) 7. (b) 8. (b) 9. (e) 10. (a) 11. (b) 12. (a) (skip this one) 13. (a) 14. (c) 15. (b) 16. (d) 17. (d) 18. (b) 19. (a) 6