Tchebysheff's Theorem

Question

Let Y be a random variable with p = 10 and o2 = 4. Use Tchebysheff’s theorem to find
a) A lower bound for P(6 < Y < 14)
b) The value of C for which P(IY – 10I greater or equal to C) less than or equal to 0.10.

Answer 1

15/16 of the data are within 4 sds of the mean 10

15/16 = 93.75% of the data

75% within 2 standard deviations from the mean

if Variance = 4, sd = 2

8 < x < 12 8 is lower bound with 75% confidence

6<x<14 with 93.75% confidence