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# ec41w10MT2_solb - Kata Bognar [email protected] Economics 41...

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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 0 ) ( 10 3 ) = 4 120 . There are ( 10 3 ) different ways in which we can select 3 calculators and there are ( 4 3 )( 6 0 ) 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 3. Which of the following is an example of a binomial experiment? C 4. We usually use the normal distribution to approximate the binomial distribution when: C 1

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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. If x is to the right of the mean then x - μ > 0 . Therefore the z-score is positive for such x values.
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