Question

Example: In a class of 3 students, the average score on the final exam is 75% and standard deviation of 5%. Amy got 80% on the final exam. How many standard deviations better than the mean is that? Mandy got 70%. How many standard deviations is Mandy's score deviate from the mean? Judy got 75%. How many standard deviation is Judy's score deviate from the mean?

Answer 1

We are given,

$\dpi{150} Mean= \mu = 75,$$\dpi{150} SD= \sigma = 5$

Q1) Now, Amy got 80% which can be expressed as

$\dpi{150} 80=75+5=\mu +1\sigma$

Hence, it is 1 standard deviation better than the mean.

Q2)Mandy got 70% which can be express as

$\dpi{150} 70=75-5=\mu -1\sigma$

Thus, Mandy's score deviates from the mean (here, less than the mean) by 1 standard deviation.

Q3) Judy got 75% which is equal to the mean i.e.

$\dpi{150} 75=\mu =\mu\pm 0\sigma$

Judy''s score does not deviate from the mean.