STT 231 Test 3: RED Give your answer in the scantron provided. Each question is worth 2 points. 1. Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qualified to serve, the City Council decides to pick the two new members randomly. What is the probability that both come from the same party? A) 9042 B) 10042 C) 9052 D)9066 E) 9052 2. Which of these has a binomial model? A) The colors of the cars in the grocery store parking lot. B) The number of black cards in a well-shuffled deck of cards C) The number of people we survey until we find someone who owns an iPod. D) The number of cards drawn from a deck until we find all four aces. E) The number of hits a baseball player gets in 6 times at bat. 3. Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap. What is the probability that you find two free ones in a 6-pack? A) 1% B) 97% C) 23% D) 13% E) 11% 4. 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 5. 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) 0.30 B) 0.15 C) 0.20 D) 0.6 6.The function 21,3)(2 xxxf is a density function. A) True B) False7. A new medicine has an 65% 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 8. 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 9. 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. 10. 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 11.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) 0.5 12. A certain population is strongly skewed to the right. 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 closer to normal. II. The sampling model of the sample means will be closer to normal. III. The variability of the sample means will be greater. A) I and III only B) I only C) III only D) II and III only E) II only 13. 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) 0.4714. 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 15. 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 Use the following to answer questions 16-18: The amount of money undergraduate students spend on books for a term has a distribution that is slightly right skewed, with a mean of $400 and a standard deviation of $80. 16. If a student is selected at random, what is the probability that this student spends more than $425 on books? A) 0.1125 B) 0.3773 C) 0.6227 D) This cannot be determined from the information given. 17. In a simple random sample of 100 undergraduate students, what is the expected value of the sample mean amount of money spent on books? A) $400 B) Anywhere between $320 and $480. C) Anywhere between $392 and $408. D) This cannot be determined from the information given. 18. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend more than $425 on books, on average? A) 0.00089 B) 0.2353 C) 0.3773 D) This cannot be determined from the information given. 19. 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 20. 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) 0.0821. 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 22. 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