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Let X be the weight in grams of a full-term newborn baby. Suppose X has a normal distribution with mean 3432 grams and standard deviation

Let X be the weight in grams of a full-term newborn baby. Suppose X has a normal distribution with mean 3432 grams and standard deviation 482 grams. Let Y=X/454 be the weight in pounds.

Show that Y also has a normal distribution.

Hint: Show that fY(y) is a normal pdf or show that M(t) is a normal mgf.

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