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Math Help - A question on Probability and deviation HELP!

  1. #1
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    A question on Probability and deviation HELP!

    1. A hospital administrator knows from past experience that the amount of resuscitation kits needed per month is (approximately) normally distributed with mean of 120 and a standard deviation of 6. Determine the probability that in a randomly selected month, the hospital will need more than 130 resuscitation kits.

    2.
    The date of births is approximately normally distributed with a mean at 280 days gestation (this is the so-called “due date”) and a standard deviation of 8 days. Suppose that a pregnant woman will have a scheduled cesarean section to deliver her baby.
    Determine how many days before the due date the cesarean section should be carried out so that there is no more than a 10 percent chance that the woman will go into labor before that date.

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  2. #2
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    #1 is simply a case of finding P(X > 130). If you are using probability tables then change to the Z variable: Z = \frac{X - \mu}{\sigma}

    #2: P(T < k) = 0.1. You need to find a value k so that 10% of gestation periods are shorter than the time k. Inverse normal distribution.

    Change to standard variable Z: P\left( Z < \frac{k - 280}{8} \right) = 0.1.

    Looking at a probability table we can see that P(0 < Z < 1.282) = 0.4. This means that P(0 > Z > -1.282) = 0.4, as the normal distribution is symmetric about the mean.

    So combining P(0 > Z > -1.282) = 0.4 and P(Z > 0) = 0.5 we get P(Z > -1.282) = 0.9 and thus P(Z < -1.282) = 0.1.

    So the value \frac{k - 280}{8} = -1.282. Now solve for k to find the answer.
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    Quote Originally Posted by nac123 View Post
    1. A hospital administrator knows from past experience that the amount of resuscitation kits needed per month is (approximately) normally distributed with mean of 120 and a standard deviation of 6. Determine the probability that in a randomly selected month, the hospital will need more than 130 resuscitation kits.

    2.
    The date of births is approximately normally distributed with a mean at 280 days gestation (this is the so-called “due date”) and a standard deviation of 8 days. Suppose that a pregnant woman will have a scheduled cesarean section to deliver her baby.
    Determine how many days before the due date the cesarean section should be carried out so that there is no more than a 10 percent chance that the woman will go into labor before that date.

    1. Calculate Pr(X > 130). Read this thread (part (a)) and do a similar thing (only the numbers change): http://www.mathhelpforum.com/math-he...tion-help.html

    2. Read this thread and do the same thing (only the numbers changes): http://www.mathhelpforum.com/math-he...tion-help.html
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