# Stat ch2 - X X X X X X X X X X X X X X X X X AP Statistics...

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XXXXXXXXXXXXXXXXXAP StatisticsSolutions to Packet 2XThe Normal DistributionsDensity Curves and the Normal DistributionStandard Normal CalculationsXXXXXXXXXXXXXX
HW #91, 2, 4, 6 - 82.1DENSITY CURVES(a) Sketch a density curve that is symmetric but has ashape different from that of the standard normal curve.
(b)Sketch a density curve that is strongly skewedto the left.2.2A UNIFORM DISTRIBUTIONThe figure below shows the density curve of auniformdistribution. The curve takes the constant value 1 over the interval from 0 to 1 and is zero outside therange of values.This means that data described by this distribution take values that are uniformlyspread between 0 and 1.Use areas under this density curve to answer the following questions.
(b)What percent of the observations lies above 0.8?
(c) What percent of the observations lie below 0.6?
(d) What percent of the observations lie between 0.25 and 0.75?
(e) What is the meanμ
2.4FINDING MEANS AND MEDIANSThe figure below displays three density curves, each withthree points indicated.At which of these points on each curve the mean and median fall?(a) mean __A___
(c) mean __A__median __B___
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2.6MEN’S HEIGHTSThe distribution of heights of adult American men is approximately normalwith mean 69 inches and standard deviation 2.5 inches.Draw a normal curve on which this mean andstandard deviation are correctly located.(Hint: Draw the curve first, locate the points where thecurvature changes, than mark the horizontal axis.)2.7MORE ON MEN’S HEIGHTSThe distribution of heights of adult American men isapproximately normal with mean 69 inches and standard deviation 2.5 inches.Use the 68–95–99.7rule to answer the following questions.(a) What percent of men are taller than 74 inches?
(b)Between what heights do the middle 95% of men fall?
(c) What percent of men are shorter than 66.5 inches?
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