A normal distribution has mean 200 and standard deviation 50. Find the area under the normal curve from the mean to 224.
A) 0.5000
B) 0.6844
C) 0.1844
D) 0.6808

Question

Quizplus · Accepted Answer

To find the area under the normal curve from the mean to a specific point, we calculate the z-score of that point and then look up the corresponding area in a standard normal distribution table or use a calculator. The z-score is calculated as $z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 224$, $\mu = 200$, and $\sigma = 50$, the z-score is $z = \frac{224 - 200}{50} = 0.48$. Looking up 0.48 in a standard normal distribution table or using a calculator gives an area of 0.1844 from the mean to $X = 224$, which is option C.

A Normal Distribution Has Mean 200 and Standard Deviation 50