3.4.5 Question Help Suppose babies born after a gestation period of 32 to 35 wee

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3.4.5

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Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 600 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 495 grams. If a 35-week gestation period baby weighs 2350 grams and a 41-week gestation period baby weighs 2550grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period?Find the corresponding z-scores. Which baby weighs relatively less?

3.4.5

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Explanation / Answer

Let X be the random variable denoting the baby weights born after a gestation period of 32 to 35 weeks. Let Y be the random variable denoting the baby weights born after a gestation period of 40 weeks.

Hence, X ~ N(2800, 600) and Y ~ N(3000, 495).

Thus, (X - 2800) / 600 ~ N(0, 1) and

(Y - 3000) / 495 ~ N(0, 1).

Hence, z-score of baby born after a 35 weeks gestation period and with a weight of 2350 grams is = (2350-2800) / 600 = -0.75. (Ans).

Hence, z-score of baby born after a 41 weeks gestation period and with a weight of 2550 grams is = (2550-3000) / 495 = -0.91. (Ans).

Since, the z-score of first baby is higher, the baby born after a 41-weeks gestation period weighs relatively less. (Ans).

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