Question

one thousand students took a test resulting in a normal distribution of the scores with a mean of 80 and a standard deviation of 5. approximately how many students scored between 75 and 85?
950
475
680
815

Explanation:

Step1: Calculate the number of standard deviations from the mean

For \(x = 75\), \(z=\frac{75 - 80}{5}=- 1\)
For \(x = 85\), \(z=\frac{85 - 80}{5}=1\)

Step2: Use the empirical rule for normal distribution

The empirical rule states that approximately \(68\%\) of the data lies within \(z=-1\) and \(z = 1\) in a normal distribution.

Step3: Calculate the number of students

If there are \(n = 1000\) students, then the number of students with scores between \(75\) and \(85\) is \(0.68\times1000=680\)

Answer:

680