Question

A distribution of values is normal with a mean of 60 and a standard deviation of 28. From this distribution, you are drawing samples of size 22. Find the interval containing the middle-most 60% of sample means: Enter your answer using interval notation. In this context, either inclusive or exclusive intervals would be acceptable. Your numbers should be accurate to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

P( < x) = 0.2

or, P(( - )/() < (x - )/()) = 0.2

or, P(Z < (x - 60)/(28/)) = 0.2

or, (x - 60)/(28/) = -0.842

or, x = -0.842 * (28/) + 60

or, x = 55.0

P( > x) = 0.2

or, P(( - )/() > (x - )/()) = 0.2

or, P(Z > (x - 60)/(28/)) = 0.2

or, P(Z < (x - 60)/(28/)) = 0.8

or, (x - 60)/(28/) = 0.84

or, x = 0.84 * (28/) + 60

or, x = 65.0