² ² ¹ b ³ ³ 55 75 55 277 00028 125 3 p x p z p z ² ²

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²² ±¨¸©¹(b)³´³´5.57.55.52.770.00281.253P xPzP z§·¨¸±²²²±¨¸¨¸¨¸©¹.(c) The mean weight of a random sample of three babies is less variable than the weight of asingle randomly-selected baby, so we are less likely to get a mean weight that is 2 pounds abovethe mean when we take a sample of three babies.
Quiz 7.3C1.(a)³´³´7.858.17.852.500.00620.1P xPzP z±§·²²² ±¨¸©¹(b)8.1xP,0.10.05xV,shape is approximately Normal since the population distribution of weights is Normal.(c)³´³´7.858.17.85500.05P xPzP z±§·²²² ±|¨¸©¹.(d)If the distribution were distinctlynon-Normal, we would not be able to calculate the probability in part (a).In part (b), the meanand standard deviation of the sampling distribution would be the same, but the shape would benon-Normal sincenis too small for the central limit theorem to apply.Thus we would also notbe able to calculate the probability in part (c).2.(a) The population would be a discreetprobability distribution with six possible outcomes—one through six—all of which had aprobability of 1/6.Thus its shape would be a uniform distribution.(b)1.713.5;0.24250xxPV.Sincen> 30, the means would be approximately Normallydistributed.(c)³´³´3.253.53.251.030.15150.242P xPzP z±§·²²² ±¨.There is roughly a 15% chanceof getting a mean of 3.25 or lower if the die is fair.(And there is roughly a 30% chance ofgetting a mean this far from 3.5 in either direction).This is not a sufficiently unusual outcomefor us to be suspicious about the fairness of this die.4¸©¹
342The Practice of Statistics, 4/e- Chapter 7© 2011 BFW Publishers
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 7343Test 7APart 11.aThis proportion is the result of a poll—a sample—so it’s a statistic.2.dThis is the definition of a sampling distribution.3.dAny time the center of a statistic’s sampling distribution is at the parameter value, thestatistic is unbiased.4.cThe mean of the sampling distribution is the same as the mean of the population, and thestandard deviation is153.25nV5.cEven if the sampling distribution is non-Normal, if the 10% condition is satisfied, this isthe appropriate formula for the standard deviation.6.aSee definition of central limit theorem on page 450 in text.7.bFor the U.S.,³´³´ˆ0.620.380.015351000pV.For Canada,³´³´ˆ0.590.410.015551000pV8.e45;3.75.xxnVPPVSincenis small and we don’t know the shape of thepopulation distribution, the shape of the sampling distribution is unknown.9.a³´8887.780.23xxP xPzPzPznPPVV§·§·¨¸¨¸§·±±±!!!!¨¸¨¸¨¸¨¸¨¸©¹¨¸¨¸©¹©¹10. e³´³´³´³´³´0.50.50.46ˆ0.510.460.54100pPpPzPzppn§·§·¨¸¨¸±±¨¸¨¸!!!¨¸¨¸±¨¸¨¸©¹©¹Part 211.(a)No.We don’t know the shape of the distribution, so we can’t calculate this probability.(b)Individual coin flips are independent. (Since the population of possible flips of this coin isinfinite, we need not be concerned about the 10% condition for finite populations.)(c)5.37.2;0.715.55xxPV(d)³´³´97.292.520.00590.715P xPzP z±§·!!!¨¸©¹.12.(a)³´³´ˆˆ0.50.50.5;0.071.50pppPV(b)Since the population of possible flips of this

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