Question

pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
a. in a letter to an advice column, a wife claimed to have given birth 309 days after a brief visit from her husband, who was working in another country. find the probability of a pregnancy lasting 309 days or longer. what does the result suggest?
b. if the length of pregnancy is in the lowest 3%, then the baby is premature. find the length that separates premature babies from those who are not considered premature.

a. the probability that a pregnancy will last 309 days or longer is .0038
(round to four decimal places as needed.)

what does the result suggest?

a. the result suggests an uncommon but not significant event occurred.
b. the result suggests the event did not occur.
c. the result suggests that the husband is the father.
d. the result suggests that either a very rare event occurred or the husband is not the father.

Explanation:

Identify the probability and context

The calculated probability of a pregnancy lasting 309 days or longer is \(0.0038\). This is an extremely low probability (\(0.38\%\)), indicating that such an event is highly unlikely to occur by chance.

Evaluate the claims

The wife claimed she gave birth 309 days after a brief visit from her husband. If the husband is the father, a very rare event (a pregnancy of 309 days or longer) must have occurred. Alternatively, if such a rare event did not occur, the husband is not the biological father.

Select the correct interpretation

Option D correctly states that the result suggests either a very rare event occurred or the husband is not the father, which is the standard logical interpretation of an extremely low probability in this context.

Answer:

• A. The result suggests an uncommon but not significant event occurred.
• B. The result suggests the event did not occur.
• C. The result suggests that the husband is the father.
• D. The result suggests that either a very rare event occurred or the husband is not the father. (Correct answer)