Assume that the distribution of the duration of human pregna

Assume that the distribution of the duration of human pregnancies can be approximated with a normal distribution with a mean of 266 days and a standard deviation of 16 days. We select 60 pregnant women at random. What is the probability that the average duration of these 60 pregnancies will be less than 260 days? The normal distribution is usually not a good approximation for the distribution of the duration of human pregnancies. In fact, the distribution is usually skewed to the left. Can you think of something that might explain the left skew of the duration of human pregnancies. Discuss. If the duration of a human pregnancy is not normally distributed, does that change your answers to parts (c) and (d)? Explain why or why not in each case.

Solution

e) this indicates that there are more number of births for the duration represent on the left side. As mentioned in the hint, this indicates that there are more number of induced labor and also speaks about more number of premature births.

f) Since the sample size is large, by the CLT, we can use the normal distribution here.