i have assignment to solve the following problem,
The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?
i tried solve the problem by first apply weak law of large numbers as follows
P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.
then, by applying WLLN
P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500
however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.