Question

It is assumed that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days. The results shown in the accompanying analysis of pregnancies were based on this normal model. The duration may not actually follow the normal model, however. Complete a and be below.

Pregnancy Analysis Results:

​i) Assuming the Normal model is​ true, 21.1% of all pregnancies last between 270 and 280 days.

​ii) Assuming the Normal model is​ true, the longest​ 25% of all pregnancies will last 276.8 days or more.

​iii) Assuming the Normal model is​ true, a sample of 60 pregnant women will have a sampling distribution with a mean of 266 days and a standard deviation of 2.07 days.

​a) Explain why the distribution may be somewhat skewed to the left. Choose the correct answer below.

A. There are more very long pregnancies than premature​ births, and it is rare for a birth to be more than two weeks premature.

B. There are more very long pregnancies than premature​ births, and there are very few pregnancies near the mean of 266 days.

C. There are more premature births than very long​ pregnancies, and nearly all pregnancies end by two weeks after the normal due date.

D. There are more premature births than very long​ pregnancies, and there are very few pregnancies near the mean of 266 days.

​b) If the correct model is in fact​ skewed, does that change the results shown in the accompanying analysis that assumed the Normal model was​ true? Explain why or why not for each.

Does the result in statement i​ change?

A. No, because the Normal model can still be used according to the Central Limit​ Theorem, even if the correct model is very skewed.

B. ​Yes, because the Normal model cannot be used if the correct model is very skewed.

C. ​Yes, because while the Normal model can still be​ used, the standard deviation will potentially change.

D. ​Yes, because while the Normal model can still be​ used, the mean will potentially change.

Does the result in statement ii​ change?

A. Yes, because the Normal model cannot be used if the correct model is very skewed.

B. Yes, because while the Normal model can still be​ used, the standard deviation will potentially change.

C. ​No, because the Normal model can still be used according to the Central Limit​ Theorem, even if the correct model is very skewed.

D. ​Yes, because while the Normal model can still be​ used, the mean will potentially change.

Does the result in statement iii​ change?

A. ​Yes, because while the Normal model can still be​ used, the standard deviation will potentially change.

B. ​No, because the Normal model can still be used according to the Central Limit​ Theorem, even if the correct model is very skewed.

C. Yes, because the Normal model cannot be used if the correct model is very skewed.

D. ​Yes, because while the Normal model can still be​ used, the mean will potentially change.

Answer 1

(a)

Correct option:

A. There are more very long pregnancies than premature​ births, and it is rare for a birth to be more than two weeks premature.

(b)

For statement (i):

B. ​Yes, because the Normal model cannot be used if the correct model is very skewed.

For statement (ii):

A. Yes, because the Normal model cannot be used if the correct model is very skewed.

For statement (iii):

B. ​No, because the Normal model can still be used according to the Central Limit​ Theorem, even if the correct model is very skewed.