Question

Distributions of gestation periods​ (lengths of​ pregnancy) for a particular animal are roughly​ bell-shaped. The mean gestation period for this animal is

268 days, and the standard deviation is 10 days for females who go into spontaneous labor. Which is more​ unusual, a baby being born 10 days early or a baby being born

10 days​ late? Explain. Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.

.A baby being born 10 days early is more unusual because its corresponding​ z-score, nothing​, is further from 0 than the corresponding​ z-score of nothing for a baby being born 10 days late. ​(Type integers or decimals rounded to two decimal places as​ needed.)

B.A baby being born 10 days late is more unusual because its corresponding​ z-score, nothing​, is further from 0 than the corresponding​ z-score of nothing

for a baby being born 10 days early. ​(Type integers or decimals rounded to two decimal places as​ needed.)

C. Both events are equally likely.

Answer 1

Solution:

Distributions of gestation periods​ (lengths of​ pregnancy) for a particular animal are roughly​ bell-shaped.

The mean gestation period for this animal is 268 days, and the standard deviation is 10 days for females who go into spontaneous labor.

Thus mean = and standard deviation =

We have to determine which is more​ unusual, a baby being born 10 days early or a baby being born 10 days​ late.

Thus x value for a baby being born 10 days early = 268 - 10 = 258 and

x value for a baby being born 10 days late = 268 + 10 = 278

Now find z scores for x values:

and

Since both x values ( baby being born 10 days early and a baby being born 10 days​ late) are 1 standard deviations from mean and are within 2 standard deviations from , thus both events are NOT unusual, that is these events are equally likely.

Thus correct option is:

C. Both events are equally likely.