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. What percent of students would expect to score between 74 and 78?

Answer 1

Step 1:

Write the given data

Step 2:

Write the z-score formula

`\begin{gathered} z\text{ = }(x-\mu)/(x) \\ \text{x = 74} \\ z\text{ = }(74-82)/(4)\text{ = }(-8)/(4)\text{ = -2} \end{gathered}`
`\begin{gathered} x\text{ = 78} \\ z\text{ = }\frac{78\text{ - 82}}{4} \\ z\text{ = }(-4)/(4)\text{ = -1} \end{gathered}`

Step 3

Draw the normal curve

P(z=-2) = 0.02275

P(z=-1) = 0.15866

Step 4:

Probability that the score is between 74 and 78 = 0.15866 - 0.02275

= 0.13591

Percentage of students would expect to score between 74 and 78

= 0.135 X 100%

= 13.5%

Final answer

13.5%