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13 July, 05:27

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean muequals 271 days and standard deviation sigmaequals 8 days.

(a) What proportion of pregnancies lasts more than 275 days?

(b) What proportion of pregnancies lasts between 267 and 273 days?

(c) What is the probability that a randomly selected pregnancy lasts no more than 261 days?

(d) A "very preterm" baby is one whose gestation period is less than 253 days. Are very preterm babies unusual?

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  1. 13 July, 05:38
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    A. 0.3085

    B. 0.3829

    C. 0.1056

    D. 0.0122. Yes, "very preterm" babies are unusual.

    Step-by-step explanation:

    A random variable X distributed approximately normal with mean mu = 271 and standard deviation sigma = 8, can be standardized by the transformation Z = (X - mu) / sigma. In this way:

    For X = 275 you have Z = (275 - 271) / 8 = 0.5

    For X = 267 you have Z = (267 - 271) / 8 = - 0.5

    For X = 273 you have Z = (273 - 271) / 8 = 0.25

    For X = 261 you have Z = (261 - 271) / 8 = - 1.25

    For X = 253 you have Z = (253 - 271) / 8 = - 2.25

    A. P (X> 275) = P (Z> 0.5) = 0.3085

    B. P (267
    C. P (X < = 261) = P (Z < = - 1.25) = 0.1056

    D. P (X < = 253) = P (Z < = - 2.25) = 0.0122. Yes, "very preterm" babies are unusual.
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