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

Assume that the duration of human pregnancies can be described by a normal model with mean 268 days and standard deviation 11 days. Answer the following questions.

a) What percentage of pregnancies should last between 265 and 275 ​days?

b) At least how many days should the longest 30% of all pregnancies​ last?

c) Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. Let y overbary represent the mean length of their pregnancies. According to the central limit​ theorem, what is the mean and standard deviation SD(y over bary​)of the normal model of the distribution of the sample​ mean,y overbary​?

​d) What is the probability that the mean duration of these​ patients' pregnancies will be less than 272 days?

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