Question 1117556
Use the normal distribution and its table of z-scores
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We are given population mean is 50 kilograms and population standard deviation is 1.25 kilograms
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a) z-score = (49.5 - 50.0) / 1.25 = -0.4
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lookup the associated probability with the calculated z-score
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Probability (P) (X < 49.5) = 0.3446
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b) P ( X > 48.5 and X < 51 ) = P (X < 51) - P (X < 48.5)
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z-score(51) = (51 - 50) / 1.25 = 0.8
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z-score(48.5) = (48.5 - 50.0) / 1.25 = -1.2
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P (X < 51) - P (X < 48.5) = 0.7881 - 0.1151 = 0.673
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c) 1 - 0.15 = 0.85
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z-score associated with probability 0.85 is 1.04
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1.04 = (X-50.0) / 1.25
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X -50.0 = 1.3
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X = 51.3 kilograms
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d)  1 - 0.02 = 0.98
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z-score associated with probability of 0.98 is 2.06
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2.06 = (52.0-50.0) / standard deviation
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standard deviation = 2 / 2.06 = 0.9708 kilograms
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