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?

Answer 1

The probability that a randomly chosen student scores 70 or below is 0.0013

Firstly, we want to calculate the z-score

We have this as;

`\begin{gathered} z-\text{score = }(x-\mu)/(\sigma) \\ \text{where x = 70} \\ \mu\text{ = mean = 82} \\ \sigma\text{ = standard deviation = 4} \\ z-\text{score = }(70-82)/(4)\text{ = -3} \end{gathered}`

Using this z-score, we proceed to calculate the probability as follows;

`P\text{ (X }\leq-3)`

We use the standard normal distribution table for this

As we can see, this z-score value falls within 3 standard deviation from the mean

According to the empirical rule, the probability value here is 0.0013