Answered

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Assume that the duration of human pregnancies can be described by a Normal model with mean days and standard deviation days.
​a) What percentage of pregnancies should last between and ​days?
​b) At least how many days should the longest ​% of all pregnancies​ last?
​c) Suppose a certain obstetrician is currently providing prenatal care to pregnant women. Let represent the mean length of their pregnancies. According to the Central Limit​ Theorem, what's the distribution of this sample​ mean, ​? Specify the​ model, mean, and standard deviation.
​d) What's the probability that the mean duration of these​ patients' pregnancies will be less than ​days?

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