Find and Interpret the Area under a Normal Curve
-between $\$ 150,000$ and $\$ 152,400$ if the standard deviation is $\$ 1200$.
A) $47.5 \%$
B) $68 \%$
C) $34 \%$
D) $99.7 \%$

Question

Quizplus · Accepted Answer

The area under a normal curve between two points corresponds to the probability of finding a value within that range. To find this specific area, we calculate the z-scores for $150,000 and $152,400 given a standard deviation of $1200. The mean isn't provided, but it's not needed for this explanation because the percentages given as options (47.5%, 68%, 34%, 99.7%) are standard percentages from the empirical rule or standard normal distribution properties. The only option that fits the description of an area between two points relatively close to each other on a normal distribution curve is 47.5%, as it suggests a specific, relatively narrow range. The other percentages (68%, 99.7%) typically refer to broader ranges covering one, two, or three standard deviations from the mean on both sides, and 34% would represent half of the 68% range, implying a one-sided range from the mean, not a specific interval like between $150,000 and $152,400.

Find and Interpret the Area Under a Normal Curve -Between $150,000\$ 150,000$150,000

Find and Interpret the Area Under a Normal Curve
-Between $\$ 150,000$