Durations of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest?b. If we stipulate that a baby is premature if the duration of pregnancy is in the lowest 3%, find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care.

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Asked Jan 25, 2020
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Durations of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest?

b. If we stipulate that a baby is premature if the duration of pregnancy is in the lowest 3%, find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care.

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Expert Answer

Step 1

a)

The random variable x represents the duration of the pregnancy.

The formula to convert the x value into z score is,

Statistics homework question answer, step 1, image 1
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Step 2

Thus, the z score is 2.67.

The probability of a pregnancy lasting 308 days or longer is obtained by finding the area to the right of 2.67.

Use Table of Standard normal (z) distribution ...

Statistics homework question answer, step 2, image 1
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