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1
Pregnancy Distribution KEY
Sample Mean
The length of human pregnancies from conception to birth varies according to a
distribution that is approximately normal with mean 266 days and standard deviation 14
days. Suppose that a random sample of 49 pregnant women were obtained and the
average length of pregnancy was recorded as 265 days.
- Clearly, with detail, and using appropriate labeling notation , sketch the distribution
of the length of human pregnancies by hand.
σ
μ
X
Length of pregnancy in days
- Clearly, with detail, and using appropriate labeling notation , sketch by hand the
distribution of the mean lengths of human pregnancies obtained from random samples
of 49 pregnant women.
n
SDx
x
σ
μ μ
x
Average pregnancy length of 49 women
2
- Use your calculator to answer the following questions. Round your answers to four decimal places.
Don’t put down just answers, i.e., show all work! a) What is the probability that a random pregnancy lasts between 200 and 300 days?
ANSWER: X distribution
normalcdf(200, 300, 266, 14) ≈ 0.9924 or 99.24%
b) What percent of mean pregnancy lengths from samples last more than 270 days?
ANSWER: x distribution
The “mean pregnancy lengths from samples” is referring to the sample means or x numbers.
normalcdf(270, 1E99, 266, 2) ≈ 0.02275 or 2.275%
c) How long do the shortest 10% of pregnancies last? Remember to use units of measure in your answer.
ANSWER: X distribution
Invnorm(0.10, 266, 14) ≈ 248.
The shortest 10% of pregnancies last 248 days or less.
d) What is the z-score for the mean pregnancy length derived from the sample at the beginning of this quiz (in the paragraph before question 1)?
ANSWER: x distribution
The mean pregnancy length at the beginning is “265 days” which refers to the “sample of 49 pregnant women.” Therefore 265 is the value of just one x number. Its z-score is
n
x z σ
μ
e) What proportion of samples have an average pregnancy length lasting less than 250 days?
ANSWER: (^) x distribution
“samples have an average pregnancy length” refers to the sample means or x numbers. The word “proportion” in the question is misleading. Replace it with “percent” and rereading it makes more sense.
normalcdf(-1E99, 250, 266, 2) (^) ≈ 0
This answer makes sense if you look at the x distribution. There we see that 250 is 8 standard deviations below the mean!
