Find and Interpret the Area under a Normal Curve
-between $\$ 150,000$ and $\$ 156,300$ if the standard deviation is $\$ 2100$.
A) $49.85 \%$
B) $99.7 \%$
C) $34 \%$
D) $47.5 \%$

Question

Quizplus · Accepted Answer

The area under a normal curve between two values represents the probability of finding a value within that range. To find this area, we calculate the z-scores for both \$150,000 and \$156,300 given a standard deviation of \$2100. The z-score formula is $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean (assumed to be \$150,000 for this calculation), and $\sigma$ is the standard deviation (\$2100). For \$156,300, the z-score is $z = \frac{(156,300 - 150,000)}{2100} = 3$. Looking up a z-score of 3 in a standard normal distribution table or using a calculator, we find that it corresponds to an area of 0.4985 or 49.85% to the left of \$156,300. This means that 49.85% of the data falls between \$150,000 and \$156,300.

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 $\$ 150,000$