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## 2.2 WS Solutions

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a) Here is a Normal curve for the distribution of batting averages. The mean and the points one, two and three standard deviations from the mean are labeled.
(b) Here is a curve showing the proportion of batting averages above 0.329. Since 0.329 is exactly two standard deviations above the mean, we know that about 95% of batting averages will be between 0.193 and 0.329. Since the curve is symmetric, half of the remaining 5%, or 2.5% should be above 0.329.
(c) Here is a curve showing the proportion of batting averages between 0.193 and 0.295. We know that about 68% of batting averages are between 0.227 and 0.295. Also, we know that half of the difference between 95% and 68% should be between 0.193 and 0.227. Therefore, about 13.5% + 68% = 81.5% of batting averages will be between 0.193 and 0.295.
#3Thethird quartile of 3 year old female heights is 97.18 cm or (calc: 97.20).The median height of 3 year old females is 94.5 cm.The girl would rank in the 24thpercentile for height of 3 year old females.The girl is 99.86 cm tall.The girl would rank in the 68thpercentilefor height of 3 year old females.(Exactcalc: 68.2)
#4
A.An IQ score of 150 is approximately the 95th percentile.B.About 22%ofpeople aged 20-34 have IQ scores between 125 and 150.C.In order to qualify for MENSA membership a person must score 162 or higher.

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