homework2_solutions - Math 1011 Intro to Statistics Spring...

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Math 1011– Intro to Statistics Spring 2011 HOMEWORK 2 Due Monday, 2/7/11 1. Suppose the average of a list of numbers is 12, and the standard deviation is 4. (a) If we add 6 to every number in the list, what are the new average and standard deviation? (b) If we multiply every number in the list by 11, what are the new average and standard deviation? (c) If we multiply every number by -2 and then add 3, what are the new average and standard deviation? Solution: (a) The average is shifted by 6 to 18, and the SD is unchanged. (b) Both are multiplied by 11, so the new average is 132 and the new SD is 44 (c) The average is multiplied by -2, and then shifted by 3. The SD is multiplied by 2, so μ = - 21 and σ = 8 2. True or false, and justify (or give a counterexample): (a) Half of the numbers in a list are always below average. (b) If a sufficiently large sample is taken, the histogram will closely follow a normal distribution. (c) If two sets of numbers both have average 50 and SD 5, then the percentage of data between 40 and 60 must be the same for both lists.
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