Assume that the duration of human pregnancies can be describ

Assume that the duration of human pregnancies can be described by a normal model with a mean of 268 days and standard deviation o17 days.

a) What percentage of pregnancies should last between 270 and 280 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 30 pregnant women. Let ybar represent the mean length of their pregnancies. According to the central theorem, what is the mean and standard deviation of the normal model of the distribution of the sample mean y?

d) What is the probability that the mean duration of these patients\' pregnancies will be less than 269 days?

Solution

a) P(270<x<280)

= P(0.12<z<0.71)

=0.2611-0.0478

= 0.2133

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b) P(Z<-0.525) = 30%

Hence no of days <259.075

or less than 259 days

c) Sample mean = same as 268

std error of sample = 17/rt of sample size

=3.104

d) P(Y<269) = P(Z<0.322) = 0.6255