MSU STT 231 - Spring 2016 (RED) (5 pages)

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 42 90 B 42 100 C 52 90 D 66 90 E 52 90 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 P Y A 0 10 1 3C 0 0 4 B 0 15 1 2C 2 0 1 C 0 20 D 0 25 5 Let X be a random variable with probability distribution table given below X P X 2 0 36 1 0 04 What is the probability that X takes a positive value A 0 30 B 0 15 6 The function f x 3x 2 1 x 2 is a density function A True B False 0 0 3 C 0 20 1 0 16 2 0 14 D 0 6 7 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 47 14 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 08 21 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 …