# Normal Distribution, Confidence Intervals

See attached file.

Normal Distribution

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. A letter was written to "Dear Abby" in which a wife claimed to have given birth 308 days after a brief visit from her husband who was serving in the Navy.

1. Find the probability of a pregnancy lasting 308 days or longer.

2. What does this result suggest?

We stipulate that a baby is premature if the length of the pregnancy is in the lowest 4%.

3. Would a baby who is born at 215 days be considered premature?

4. Find the length of pregnancy that separates premature babies from those who are not premature.

Student t Distribution - Confidence Intervals

A simple random sample of the body temperatures of 106 healthy humans were taken for which

x=98.20o F and s=0.62oF .

1. What two requirements must be satisfied to use a Student t distribution.

2. Determine the number of degrees of freedom for this sample size.

3. Construct a 99% confidence interval to estimate the mean body temperature of all healthy humans.

4. What does the confidence interval suggest about the use of 98.6o as the mean body

temperature.

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.