Question

A geologist is attempting to measure the distance between two mountain peaks by taking the average of a series of measurements. Each measurement X, is an i.i.d. random variable with meand and variance of 4 inches. Using Chebyshev's inequality, how many measurements must the geologist make in order to be 95% certain that the value he obtains is within 1/10 inch of the actual distance?

Answer 1

Answer:

Given,

P(|X-$\mu$|<=e) >= 1 - $\sigma ^{2}$ / (ne²)

here e = 1/10 inch of actual distance

Consider,

1 - $\sigma ^{2}$ / (ne²) =0.95

$\sigma ^{2}$ / (ne²) = 0.05

4/(n*(1/10)²) = 0.05

n = 8000