2. Assume that the duration of human pregnancies can be described by a normal model with mean 266 days and standard devi

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2. Assume that the duration of human pregnancies can be
described by a normal model with mean 266 days and standard
deviation of 16 days.
(a) What percentage of pregnancies should last between 270 and
280 days?
(b) At least how many days should the longest 25% of all
pregnancies last?
(c) Suppose a certain obstetrician is currently providing
prenatal care to 60 pregnant women. Let represent the mean length
of their pregnancies. According to the Central Limit Theorem,
what’s the distribution of the sample mean, ? Specify the model,
mean, and standard deviation.
(d) What is the probability that the mean duration of these
patient’s pregnancies will be less than 260 days?