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?

Question

asked Aug 19, 2019 193k views

1 Answer

Nahshon Paz · Answer 1 · 2019-08-23T19:07:42+0000

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