Question

Given a mean of 24.5 and a standard deviation of 1.7, within how many standard deviations of the mean do the values 24, 23, 28, 23, 24, and 25 fall?

Answer 1

It would be 3. I hope this helps!

Answer 2

Given mean = 24.5 and standard deviation = 1.7

Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].

Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].

Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].

Given values are 24, 23, 28, 23, 24, and 25.

So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.