Question

a set of physics exam scores are normally distributed with a mean of 80 points and a standard deviation of 6 points. irina got a score of 95 points on the exam. what proportion of exam scores are lower than irinas 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 from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $x = 95$, $\mu=80$, and $\sigma = 6$. So, $z=\frac{95 - 80}{6}=\frac{15}{6}=2.5$.

Step2: Find the proportion using the standard normal table

The standard - normal table gives the cumulative distribution function of the standard normal distribution. Looking up the z - score of 2.5 in the standard normal table, we find the proportion of values less than $z = 2.5$. The value corresponding to $z = 2.5$ in the standard normal table is 0.9938.

Answer:

0.9938