Question 1.PR.11: On a test taken by 100 students, the average mark is 65, wit...

(a) z = 1.5 and −1.5 respectively.
(b) Using Chebyshev’s theorem with k = 1.5, we have that at least (1 − 1/1.5²) = 0.56 (56%) lies within 1.5 standard deviations of the mean, so at most 0.44 (44 students) lies outside the range.
(c) Chebyshev’s theorem applies to both tails, so we cannot answer this part. You cannot halve the figure of 0.44 because the distribution may be skewed.