The length of human pregnancies is approximately normally distributed with mean 273 days and standard deviation 16 days. A pregnancy that lasts less than 259 days is considered as �pre-term� and a pregnancy that lasts more than 280 days is considered as �late-term�. Show your work or calculator command.

a. What is the probability that a randomly selected pregnancy is �pre-term�?

b. What is the probability that a randomly selected pregnancy is �late-term�?

c. 20% of all pregnancies last less than how many days of gestation?

d. The longest 5% pregnancies last more than how many days?

e. If samples of 64 pregnant women are randomly selected, what is the mean and standard deviation of the sampling distribution of sample mean pregnancy days? (Use correct symbols to report your answer)

f. What is the probability that a random sample of 64 pregnant women has a mean gestation period of less than 266 days?

g. What is the probability that a random sample of 64 pregnant women has a mean gestation period of more than 282 days?