3.Assume that the duration of human pregnancies can be described by a Normal model with mean 265 days and standard deviation 18 days.

a) What percentage of pregnancies should last between 267 and 275 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 56 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 254 days?

3a.A man recorded the speeds of cars driving past hishouse, where the speed limit was 35 mph. The mean of 100 readings was 38.79 mph with a standard deviation of 3.72 mph.(He actually recorded every car for atwo-month period. These are 100 representativereadings.)

a) How many standard deviations from the mean would a car going the speed limitbe?

a) A car traveling at the speed limit is nothing standard deviations from the mean.

b) Which would be moreunusual, a car traveling 48 mph or one going 24 mph?