In: Statistics and Probability
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 266 days and a standard deviation of 8 days. (a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 4% of pregnancy lengths?
Answer:
Given that:
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 266 days and a standard deviation of 8 days
a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths?
The distribution of the 11% is
Using Z -score formula
The minimum pregnancy length is 275.8 days
b) What is the maximum pregnancy length that can be in the bottom 4% of pregnancy lengths?
The distribution of the 4% is
Using Z -score formula
The minimum pregnancy length is 251.9 days