Question

The average and standard deviation of a measurement is 15.0 ± 5.0. if 100 students measured the value, how many would you expect to get a value greater than 20?

Answer 1

Solution: We are given:

`\mu=15, \sigma=5`

Using the empirical rule, we have:

`\mu \pm \sigma` covers 68% of data.

Also the percentage of values below mean = Percentage of values above mean = 50%

Now, let's find the z score for x=20

`z=(20-15)/(5)=1`

Therefore, the percentage of values greater than 1 standard deviation above mean
`50\% - (68\%)/(2) =50\%-34\%=16%`

Expected number of students = 16% of 100 = 16