Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 123 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 262 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length. Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.

(Note: The critical
z
-value to use,
z
c
, is: 2.576)

( , )

Your answer should be rounded to 3 decimal places.