# hw_week_4 - Answered - DUE Date: 9/23 Make sure to show all...

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DUE Date: 9/23 Name:________________________ Make sure to show all work. Homework for Week 4 When a series of values takes on some distribution, it is common to describe it in terms of a distribution and parameters that fit the data. IQ tests, for example, are rescaled so that results are normally distributed with a mean of 100 and a standard deviation of 15. Taken a step further, this implies that about 99.5% of people who take an IQ test will get a score between 55 and 145, about 95% between 70 and 130, and so on. You may see IQ ~ Normal( μ =100, σ 2 =225) as shorthand for “we think IQ is normally distributed with mean 100 and variance 225”. If you find this helpful in keeping important numbers organized, then by all means, use it. 1) In a normal distribution, what proportion of the scores fall within the interval between μ and one standard deviation above μ ? (Equivalently, in the IQ example above, what fraction of the population would you expect to score between 100 and 115?) a. .8413 b. .6826 c. .4143 d. .1359 e. .3414 2) In a normal distribution, .9544 of the scores will be located in the interval between __. a. μ plus 2σ b. μ plus 1σ and μ minus 2σ c. μ plus 2σ and μ minus 3σ d. μ plus 2σ and μ minus 2σ e. μ plus 1σ 3) If a distribution is normal with µ = 50 and σ = 10, then what proportion of the scores will fall between 40 and 60 (µ ± σ)? a. .1359

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## This note was uploaded on 03/27/2010 for the course HP 340L at USC.

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hw_week_4 - Answered - DUE Date: 9/23 Make sure to show all...

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