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Unformatted text preview: Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Winter 2010 Second Midterm- suggested solutions - Part I - Multiple Choice Questions (3 points each) 1. A sample of 3 different calculators is randomly selected from a box containing 4 defective and 6 non-defective calculators. The probability that at least 2 of the 3 calculators is defective is B (a) 1/2 (b) 1/3 (c) 2/3 (d) 3/10 Explanation: X : the number of defective calculators in a sample of 3 different calculators. The probability that at least 2 out of the 3 calculators is defective is P ( X ≥ 2) = P ( X = 3)+ P ( X = 2) . P ( X = 2) = ( 4 2 )( 6 1 ) ( 10 3 ) = 36 120 . There are ( 10 3 ) different ways in which we can select 3 calculators and there are ( 4 2 )( 6 1 ) different ways in which we can select 2 defective and 1 non-defective calculators. P ( X = 3) = ( 4 3 )( 6 ) ( 10 3 ) = 4 120 . There are ( 10 3 ) different ways in which we can select 3 calculators and there are ( 4 3 )( 6 ) different ways in which we can select 3 defective calculators. Hence P ( X ≥ 2) = 1 3 . 2. Thirty two percent of adults did not visit their physicians’ offices last year. Let X be the number of adults in a random sample of 15 adults who did not visit their physicians’ offices last year. The standard deviation of the probability distribution of X is approximately: D (a) 3.26 (b) 4.80 (c) 3.20 (d) 1.81 Explanation: X follows a binomial distribution with parameters n = 15 and p = 0 . 32 . Therefore the standard deviation of X is p np (1- p ) = √ 15 · . 32 · . 68 = 1 . 806654367 ≈ 1 . 81 . 3. Which of the following is an example of a binomial experiment? C (a) Rolling a die 10 times and observing for the number rolled (b) Selecting five persons and observing whether they are in favor of an issue, against it, or have no opinion (c) Tossing a coin 20 times and observing for a head or a tail (d) Drawing three marbles from a box that contains red, blue, and yellow marbles Explanation: A binomial experiment is a sequence of independent Bernoulli trials, i.e. each trial has two possible outcomes. The trial described in parts (a), (b) and (d) have more than two possible outcomes. 4. We usually use the normal distribution to approximate the binomial distribution when: C (a) the sample size is at least 30 (b) np and n (1- p ) are both less than 5 1 (c) np and n (1- p ) are both greater than 5 (d) nx is greater than 30 Explanation: see the procedure on page 318. 5. For a normal distribution, the z-score for an x value that is to the right of the mean is always: D (a) equal to zero (b) negative (c) greater than 1 (d) positive Explanation: Assume a random variable X with a mean μ and a standard deviation σ. The z-score corresponding to an x value of X is z = x- μ σ . The standard deviation is always positive....
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This note was uploaded on 05/31/2010 for the course ECON 41 taught by Professor Guggenberger during the Spring '07 term at UCLA.
- Spring '07