In: Statistics and Probability
Use the following information for all remaining questions on this worksheet.
The lengths of human pregnancies are normally
distributed with a mean of 268 days and a standard deviation of 15
days.
1.a) If one pregnant woman is randomly selected, find the
probability that her pregnancy lasts less than 260 days. Round your
result to 4 decimal places.
a. 0.2969
b. 0.7031
c. 0.5000
d. 0.2742
1.b) Is it unusual for one woman to have a pregnancy that
lasts less than 260 days?
a. No, the probability is greater than 0.05.
b. Yes, the probability is greater than 0.05.
c. Yes, the probability is less than 0.05.
d. No, the probability is less than 0.05.
1.c) Complete the following sentence: If we looked at a
random sample of 100 pregnant women would expect ____ to
have pregnancies lasting less than 100 days.
a. 29 or 30
b. 27 or 28
c. about 50
d. 71 or 72
1. d) A researcher chooses a sample of 25
pregnant women and wants to look at the mean length of the
pregnancies for the sample. Does the Central Limit Theorem Apply?
Briefly explain why or why not.
1.e) What is the probability that a randomly selected sample of 25
pregnant women have a mean length of pregnancy less than 260 days?
Round your response to 4 decimal places.
1.f) Based on your response to the previous question, is it unusual
for a random sample of 25 women to have a mean length of pregnancy
of less than 260 days? Explain your response in a full
sentence.
1.g) If a random sample of 25 pregnant women had a mean length of
pregnancy of less than 260 days, does that mean that all 25 women
had a pregnancy that lasted less than 260 days? Explain your
response in a full sentence.