value: 4 mr. emmer gave a test in his chemist...
value: 4 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 = (x - μ)/σ where x is the given value, μ is the mean and σ 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
Answer
# Explanation:
## Step1: Calculate the z - score
Given $x = 70$, $\mu=82$, $\sigma = 4$. Using the 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, the probability corresponding to $z=-3$ is $0.0013$.
# Answer:
a..0013