Question

From a sample with n=40, the mean duration of a? geyser's eruptions is 3.36 minutes and the standard deviation is 0.53 minutes. Using? Chebychev's Theorem, determine at least how many of the eruptions lasted between 2.3 and 4.42 minutes.

At least____________of the eruptions lasted between 2.3 and 4.42 minutes.

Answer 1

Let X denote the time for which the geyser's eruptions lasted.

Given: Mean,u = 3.36 minutes

Standard deviation,s = 0.53 minutes

Using Chebyschev's inequality, for k > 0

P(|X - u| < ks) >= 1 - (1/k^2)

For k = 2,

P(|X - 3.36| < 2*0.53) >= 1 - (1/2^2)

-> P(2.3 < X <4.42) >= 3/4

Thus, there is atleast a probability of 75% that the eruptions lasted between 2.3 and 4.42 minutes

So for a sample of40, 0.75 of it which is 30.

At least 30 of the eruptions lasted between 2.3 and 4.42 minutes.