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Math Help - proportion and distribution

  1. #1
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    proportion and distribution

    The duration of pregnancy in humans is approximately Normally distributed with μ = 266 days and σ = 16 days. In the following questions, assume that this distribution is exact.

    (a) What proportion of pregnancies last between 250 and 290 days?

    (b) A post-term pregnancy is defined as one that lasts more than 294 days. What proportion of pregnancies are post-term?

    (c) What durations give the quartiles of the distribution of human pregnancy durations?
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  2. #2
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    If 'X' is a random variable which denotes 'duration of pregnancy in humans', then X\sim N(\mu=266, \sigma^2=16^2).

    (a) Required to find P(250<X<290)

    = P(\frac{250-266}{16}<\frac{X-266}{16}<\frac{290-266}{16})

    = P(-1<Z<1.5)=\Phi(1.5)-\Phi(-1)=\Phi(1.5)-1+\Phi(1) (put the values)

    (b) Required to find P(X>294)

    =P(\frac{X-266}{16}>\frac{294-266}{16})

    = 1-\Phi(1.75) (put the value)

    (c) Find Q's such that P(X<Q_1)=0.25, P(X<Q_3)=0.75 while Q_2 is \mu=266


    "Standardization" has been done in (a) and (b); Z is a standard normal variate and \Phi(.) denotes the CDF of a standard normal distribution.
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    what do you mean by ("put the value")? and i don't understand (c)
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  4. #4
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    Quote Originally Posted by sanja85 View Post
    what do you mean by ("put the value")? and i don't understand (c)
    To better understand the help you have been given, it might be best at this stage to go back and review this material in your class notes and textbook.
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  5. #5
    Senior Member Sambit's Avatar
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    Quote Originally Posted by sanja85 View Post
    what do you mean by ("put the value")? and i don't understand (c)
    I mean put the values of \Phi(1),\Phi(1.5) etc. these are the values of a standard normal cdf. A standard textbook should have a table containing these values in its appendix.
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  6. #6
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    1.5-1+(1) would be
    0.9332-1+0.8413
    which then equals
    0.7745
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