statistics homework problem ?

the lengths of a particular animal’s pregnancies are approximately normally distributed, with mean = 276 days and standard deviation = 20 days. 

A) what proportion of pregnancies lasts more than 281 days?

B) what proportion of pregnancies lasts between 271 and 291 days?

C) what is the probability that a randomly selected pregnancy lasts no more than 236 days?

D) a “very preterm” baby is one whose gestation period is less than 246 days. are very preterm babies unusual?

1 Answer

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  • 4 months ago

    A) P(x > 281) => P(z > (281 - 276)/20)

    so, P(z > 0.25) => 1 - P(z < 0.25)

    From tables we get:

    1 - 0.5987 = 0.4013

    i.e. about 40%

    B) P(271 < x < 291)

    i.e.  P[(271 - 276)/20 < z < (291 - 276)/20]

    so, P(-0.25 < z < 0.75)

    or, P(z < 0.75) - P(z < -0.25)

    or, P(z < 0.75) - P(z > 0.25)

    i.e. P(z < 0.75) - (1 - P(z < 0.25))

    so, P(z < 0.75) + P(z < 0.25) - 1

    From tables we get:

    0.7734 + 0.5987 - 1

    so, 0.3721

    i.e. about 37%

    C) P(x < 236) => P(z < (236 - 276)/20)

    i.e. P(z < -2)

    or, P(z > 2) => 1 - P(z < 2)

    From tables we get:

    1 - 0.9772 = 0.0228

    so, about 2.3%

    D) P(x < 246) => P(z < (246 - 276)/20)

    i.e. P(z < -1.5)

    or, P(z > 1.5) => 1 - P(z < 1.5)

    From tables we get:

    1 - 0.9332 = 0.0668

    i.e. about 7%....unusual to expect.

    :)>

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