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In: Statistics and Probability

Use the following information for all remaining questions on this worksheet. The lengths of human pregnancies...

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.

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.

b. Is it unusual for one woman to have a pregnancy that lasts less than 260 days?

c. If we looked at a random sample of 100 pregnant women would expect_____to have pregnancies lasting less than 100 days.

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.

e. For groups of 25 women, find the mean and standard error for the sampling distribution of the mean length of pregnancy. Round the value to one decimal place, if rounding is necessary. Be sure to include units.

mean: (select)

  1. 268
  1. Days
  1. 10.7
  1. Women
  1. 53.6
  1. Pregnancies
  1. 253

standard error: (select)

  1. 3
  1. Days
  1. 15
  1. Women
  1. 25
  1. Pregnancies
  1. 17.9

f. 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.

g. 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.

h. 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.

i. For random samples of 25 pregnant women, 95% of all sample means for the mean length of pregnancy will fall between __ days and ___days?

  

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orchestra answered 2 years ago
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