STT 231 Test 3: YELLOW Give your answer in the scantron provided. Each question is worth 2 points. 1) The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? A) 1/2 B) 4/9 C) 5/8 D) 7/8 E) 5/9 2) Which of these random variables has a binomial model? A) The number of aces in a well-shuffled deck. B) The number of black cards in a well-shuffled deck. C) The number of Democrats among a group of 20 randomly chosen adults. D) The number of cars inspected until we find three with bad mufflers. E) The number of people we check until we find someone with green eyes. 3) An ice cream stand reports that 12% of the cones they sell are "jumbo" size. You want to see what a "jumbo" cone looks like, so you stand and watch the sales for a while. What is the probability that there is exactly 1 jumbo among the first 6 cones sold by the ice cream stand A) 12% B) 54% C) 6% D) 38% E) 84% 4. In a box, there are 10 red balls and 10 green balls. You select three balls without replacement. To calculate the probability of getting at least two red balls, we can use the hypergeometric model. A) True B) False 5. Which of the following is true in a binomial distribution? A) Each outcome is dependent on the previous outcome. B) There are only two outcomes in each trial. C) The probability of success changes from trial to trial. D) The outcome of a trial depends on the number of trials. E) Both A and C are true. 6. A new medicine has an 85% success rate. Twenty patients are treated with it. What is the probability that exactly eighteen are cured with this new medicine? A) 0.054 B) 0.7707 C) 0.2293 D) 0.0012 E) none of these numbers 7. We select a jury of 12 from 15 potential jurors (9 women and 6 men). What is the probability of having 7 women in this jury A) 0.00131 B) 0.99869 C) 0.4747 D) 1 E) 0.58. A new medicine has an 85% success rate. Five patients are treated with it. Each patient’s conditions improves/worsens independent of the other patients. You want to compute the probability that exactly four of the five patients are cured. What probability model will you use for this? A) The exponential probability model B) The uniform probability model C) The hypergeometric probability model D) The capture-recapture model E) The binomial probability model Use the following to answer questions 9 & 10. Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semester. Value of X 3 4 5 6 Probability of X 0.07 0.4 0.25 0.28 9. What is the average number of courses full-time students at this college take this semester? A) 4 classes B) 4.26 classes C) 4.74 classes D) 5 classes 10. What is the standard deviation of the number of courses full-time students at this college take this semester? A) 0.89 classes B) 0.94 classes C) 1 class D) 23.36 classes 11. Let Y be a random variable that takes values -1, 0, 1, 2 with probabilities 3C, 0.4, 2C and 0.1 respectively. If the table is a probability distribution table, find the value of C Y -1 0 1 2 P(Y) 3C 0.4 2C 0.1 A) 0.10 B) 0.15 C) 0.20 D) 0.25 12. Let X be a random variable with probability distribution table given below: X -2 -1 0 1 2 P(X) 0.36 0.04 0.3 0.16 0.14 What is the probability that X takes a positive value? A) 0.60 B) 0.15 C) 0.20 D) 0.3 13.The function 21,3)(2 xxxf is a density function. A) True B) False14. A certain population is bimodal. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be more clearly bimodal. II. The sampling distribution of the sample means will be approximately normal. III. The variability of the sample means will be smaller. A) I only B) II only C) I, II, and III D) II and III E) III only 15. The weight of apples in a farm is normally distributed, with a mean of 110 grams, and a standard deviation of 15 grams. Find the probability that an apple selected at random will weigh between 95 and 115 grams. A) 0.84 B) 0.53 C) 0.16 D) 0.47 16. IQ scores are normally distributed with mean 100 and a standard deviation of 12. If a university offers scholarships for first year students whose IQ score is in the top 3%, what is the minimum IQ score that a student must have to qualify for these scholarships? A) 77 B) 123 C) 120 D) 110 17. The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. What is the probability that a person is served in less than 3 minutes? A) 0.999 B) 0.25 C) 0.47 D) 0.53 E) 0.75 18. Which of the following random variables has a symmetric density graph? A) The standard normal random variable B) The exponential random variable C) The uniform random variable D) All but B E) All 19. Find the probability that a standard normal random variable has a value greater than - 1.75 A) 0.96 B) 0.04 C) 0.92 D) 0.08 20. Let Z be a standard normal random variable. Find P(-2.5< Z < 2.5). A) 0.05 B) 0.01 C) 0.90 D) 0.006 E) 0.9876 21. The amount of time it takes to take an exam has a skewed-to-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes. A sample will be selected at random from the entire population. If we decide to choose a random sample of 9 students, which of the following properly describes the sampling distribution of the sample mean for 9 students? A) It is the distribution of a data set of 9 student's time. B) It is normally distributed with mean 65 minutes and s.d. of mean is 8/3 minutes. C) Its distribution has a mean of 65 minutes and standard deviation of 8/3 minutes, but the shape of the distribution is still skewed-t-left. D) Its distribution has a mean of 65 minutes and standard deviation of 8 minutes, but the shape of the distribution is still skewed-t-left.22. A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. The fitness