Assume that the duration of human pregnancies can be described by a Normal model with mean 267 days and standard deviation 14 days.

a) What percentage of pregnancies should last between 273 and 283 days?

b) At least how many days should the longest 20% of all pregnancieslast?

c) Suppose a certain obstetrician is currently providing prenatal care to 53 pregnant women. Let y represent the mean length of their pregnancies. According to the Central LimitTheorem, what's the distribution of this samplemean, y? Specify themodel, mean, and standard deviation.

d) What's the probability that the mean duration of thesepatients' pregnancies will be less than 260 days?