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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?

Respuesta :

Solution: We are given:

[tex]\mu=15, \sigma=5[/tex]

Using the empirical rule, we have:

[tex]\mu \pm \sigma[/tex] 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

[tex]z=\frac{20-15}{5}=1[/tex]

Therefore, the percentage of values greater than 1 standard deviation above mean [tex]50\% - \frac{68\%}{2} =50\%-34\%=16%[/tex]

Expected number of students = 16% of 100 = 16


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