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assume that the duration of human pregnancies can be described by a normal model with a...

assume that the duration of human pregnancies can be described by a normal model with a mean of 268 days in the standard deviation of 17 days.
a.) what percentage of pregnancies should last between 274 and 281 days?
b.) at least how many days should the longest 15% of all pregnancies last?
c.) suppose a certain obstetrician is currently providing prenatal care to 73 pregnant women, let Y represent the mean length of their pregnancies. according to the central limit theorem, what is the distribution of this sample mean, y? specify the model, mean, and standard deviation.
d.) what’s the probability that the mean duration of these pregnancies will be less than 260 days?
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