Question

mr. emmer gave a test in his chemistry class. the scores were normally distributed with a mean of 82 and a standard deviation of 4. a student is randomly chosen. what is the probability that the student scores a 70 or below? use the formula for a z - score $z=\frac{x - mu}{sigma}$ where x is the given value, $mu$ is the mean and $sigma$ is the standard deviation. then refer to the chart on page 11 of the lesson to find the probability.

a..0013
b..0179
c..0668
d..5000

Explanation:

Step1: Calculate the z - score

Given $x = 70$, $\mu=82$, $\sigma = 4$. Using the z - score formula $z=\frac{x - \mu}{\sigma}$, we have $z=\frac{70 - 82}{4}=\frac{- 12}{4}=-3$.

Step2: Find the probability from the z - table

Looking up the z - score of $- 3$ in the standard normal distribution table (z - table), the probability corresponding to $z=-3$ is $0.0013$.

Answer:

A. 0.0013