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 Cam's score?**
*You may round your answer to four decimal places.*

To find the proportion of exam scores higher than Cam's score, we'll first calculate the z-score for Cam's score and then use the z-score to find the corresponding proportion from the standard normal distribution.

The z-score is calculated as follows:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- \( X = 65 \) (Cam's score)
- \( \mu = 70 \) (mean score)
- \( \sigma = 4 \) (standard deviation)

Substituting the values:

\[
z = \frac{65 - 70}{4} = \frac{-5}{4} = -1.25
\]

Next, we'll find the proportion of the distribution that corresponds to a z-score of \(-1.25\). This can be looked up in the standard normal distribution table, or calculated using a statistical function.

The cumulative probability for \( z = -1.25 \) gives the proportion of exam scores less than Cam's score. To find the proportion of scores higher than Cam's score, subtract this value from 1.

The cumulative probability for \( z = -1.25 \) is approximately 0.1056.

Therefore, the proportion of exam scores higher than Cam's score is:

\[
1 - 0.1056 = 0.8944
\]

So, **0.8944** of the exam scores are higher than Cam's score.

Learn how to calculate the proportion of exam scores higher than Cam's score of 65 points in a normally distributed set with mean 70 and standard deviation 4. Detailed solution with step-by-step calculation using the z-score formula.

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