I need help with this question please

label Statistics
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The mean human gestation period is 266 days. Actual time to delivery is approximately normally distributed with a standard deviation of about 12 days. Marcelle goes into labor and gives birth to a child 245 days after conception. What percentage of women give birth (a) at the same point in pregnancy as or earlier than Marcelle, (b) at a later point in pregnancy than Marcelle, and (c) between their due date and the point at which Marcelle gave birth?

May 13th, 2015

Since we are dealing with a normal distribution we can use the Normal Distribution Curve which has very specific values of probability.

First we find the Z value which represents the number of standard deviations away from the mean:

245 - 266 / 12 = - 1.75

Now we look up that value on the Z chart to find the probability, so

a)  P = 0.0401 which represents 4.01%

b) at a later point we have to subtract that P value from the whole, or 1

therefore, 1 - 0.0401 = 0.9599 = 95.99%

c) this question does not give a specific due date, so we assume the mean:

between the mean and Marcelle's due date, we calculate

0.500 - 0.0401 = 0.4599 = 45.99%

May 13th, 2015

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May 13th, 2015
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May 13th, 2015
Jun 22nd, 2017
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