Answer:
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.
