Question

a set of chemistry exam scores are normally distributed with a mean of 70 points and a standard deviation of 4 points. cam got a score of 65 points on the exam. what proportion of exam scores are higher than cams score? you may round your answer to four decimal places.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $x = 65$, $\mu=70$, and $\sigma = 4$. So, $z=\frac{65 - 70}{4}=\frac{- 5}{4}=-1.25$.

Step2: Find the proportion of scores lower than Cam's

We use the standard normal distribution table (or z - table) to find the proportion of values corresponding to $z=-1.25$. Looking up $z = - 1.25$ in the z - table, we get $P(Z < - 1.25)=0.1056$.

Step3: Find the proportion of scores higher than Cam's

Since the total area under the normal - distribution curve is 1, the proportion of scores higher than Cam's is $P(Z>-1.25)=1 - P(Z < - 1.25)$. So, $P(Z>-1.25)=1 - 0.1056 = 0.8944$.

Answer:

$0.8944$