Newborn babies in the United States have a mean birth weight of 7.5 pounds and a standard deviation of 1.25 pounds. Assume the data possesses a bell-shaped distribution.

A. What are the upper and lower limits of the interval that contains 95% of all newborns in the United States?

B. Does a newborn with a birth weight of 4.5 pounds fall within an interval which contains 95% of all newborn birth weights. Why or why not?

A.

Lower limit: 5 pounds

Upper limit: 10 pounds

B.

4.5 is more than two standard deviations from the mean, so it does not fall within an interval which contains 95% of all newborn birth weights.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5

Standard deviation = 1.25

A. What are the upper and lower limits of the interval that contains 95% of all newborns in the United States?

By the Empirical Rule, within 2 standard deviations of the mean.

Lower limit: 7.5 - 2*1.25 = 5 pounds

Upper limit: 7.5 + 2*1.25 = 10 pounds

B. Does a newborn with a birth weight of 4.5 pounds fall within an interval which contains 95% of all newborn birth weights. Why or why not?

4.5 is more than two standard deviations from the mean, so it does not fall within an interval which contains 95% of all newborn birth weights.