"According to the National Center for Health Statistics, in 2005 the average birthweight of a newborn baby was approximately normally distributed with a mean of 119 ounces (7 lb, 7 oz) and a standard deviation of 19 ounces." What percentage of babies weigh between 112 and 144 ounces (7 and 9 lb) at birth?
A) 9.34%
B) 14.43%
C) 44.91%
D) 55.09%

Question

Quizplus · Accepted Answer

To find the percentage of babies weighing between 112 and 144 ounces, we convert these values to z-scores using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 112 ounces, $z = \frac{(112 - 119)}{19} = -0.37$, and for 144 ounces, $z = \frac{(144 - 119)}{19} = 1.32$. Looking these z-scores up in a standard normal distribution table, we find that the percentages are approximately 35.62% for -0.37 and 90.71% for 1.32. The difference, 90.71% - 35.62%, gives us approximately 55.09%, which represents the percentage of babies weighing between 112 and 144 ounces.