A probability distribution has a mean of 45 and a standard deviation of 1. Use Chebychev's inequality to estimate the probability that an outcome of the experiment lies between 43 and 47.
A) At least 0.04
B) At least 0.25
C) At least 0.75
D) At least 0.5
E) At least 0.8

Question

Quizplus · Accepted Answer

Chebychev's inequality states that for any distribution, the proportion of outcomes within k standard deviations of the mean is at least 1 - 1/k^2. Here, 43 to 47 is within 2 standard deviations (since the mean is 45 and the standard deviation is 1), so k = 2. Thus, the probability is at least 1 - 1/(2^2) = 1 - 1/4 = 0.75.

A Probability Distribution Has a Mean of 45 and a Standard