The lengths of pregnancies are normally distributed with a mean of 280 days and a standard deviation of 16 days. (a) Find the probability that an individual woman has a pregnancy shorter than 271 days.

MATLAB: An Introduction with Applications
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The lengths of pregnancies are normally distributed with a mean of 280 days and a standard
deviation of 16 days.
(a) Find the probability that an individual woman has a pregnancy shorter than 271 days.
(b) If 25 women are randomly selected, find the probability that they have a mean preg-
nancy shorter than 271 days.
(c) There should be a difference in your method for the previous two questions. Explain
what you did differently for each problem and explain WHY your answers are different.
(d) Find the probability that an individual woman has a pregnancy longer than 300 days.
(e) Find the probability that an individual woman has a pregnancy between 280 and 300
days.
(f) What is the cutoff number of days for a pregnancy for the top 15% of women?
(g) What is the cutoff number of days for a pregnancy for the bottom 20% of women?
Transcribed Image Text:The lengths of pregnancies are normally distributed with a mean of 280 days and a standard deviation of 16 days. (a) Find the probability that an individual woman has a pregnancy shorter than 271 days. (b) If 25 women are randomly selected, find the probability that they have a mean preg- nancy shorter than 271 days. (c) There should be a difference in your method for the previous two questions. Explain what you did differently for each problem and explain WHY your answers are different. (d) Find the probability that an individual woman has a pregnancy longer than 300 days. (e) Find the probability that an individual woman has a pregnancy between 280 and 300 days. (f) What is the cutoff number of days for a pregnancy for the top 15% of women? (g) What is the cutoff number of days for a pregnancy for the bottom 20% of women?
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