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Question 283:



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You'll need to find the area under the normal curve between the mean 264 and 266 days. Since we're finding the probability of a sample mean instead of a single data point we need to adjust the z-score formula a bit. Instead of (x-mean)/sd we divide by the standard error of the mean (SEM) which is the standard deviation dived by the square root of the sample size. This gets us : 25/SQRT(100) = 25/10 = 2.5. Now we compute the z-score using this value in the denominator instead of the population sd of 25.

First we find the larger area, then the smaller area and subtract our the smaller area from the laerger to find the area in betwee.  The z-score of 266 days is (266-264)/2.5 = .80, to find the area use the z-score to percentile calculator and enter .80 with one-sided area. You should get about 78.81%. So the probability of having a pregnancy of 266 days or less is ~79%.

The probability of having a pregnancy up to 264 days is (264-264)/2.5 = 0 and a z-score of zero has a probability of 50%.  Subtracting 50% from 78.81% gets us 28.81%. So the probability of a sample of 100 having a mean pregnancy between 264 and 266 days is .2881.

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