SOLUTION: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Out of 50 pregnancies how many would you expect to last less than

Question 1128745: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Out of 50 pregnancies how many would you expect to last less than 250 days? My answer was -14.53. I do not believe it is correct. Please help, and thank you.
The lengths of pregnancies of human are normally distributed with a mean of 268 days and a standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of babies are born prematurely?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
z-score = (250 - 268) / 15 = -1.2
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the probability(P) associated with a z-score of -1.2 is determined from the table of z-scores
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P(X < 250) = 0.1151
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50 * 0.1151 = 5.755 is approximately 6 pregnancies less than 250 days
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268 - (7 * 3) = 247 days
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we use the normal distribution to approximate 247
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P(X = 247) = P(X < 247.5) - P(X < 246.5)
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z-score(247.5) = (247.5 - 268) / 15 is approximately -1.37
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z-score(246.5) = (246.5 - 268) / 15 is approximately -1.43
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P(X = 247) = 0.0853 - 0.0764 = 0.0089 is approximately 1%
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