Calculate the probability of a result falling within 2.5 standard deviations from the mean, using
a) Chebyshev’s Theorem
b) Empirical Rule
Please help
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a) Chebyshev's inequality tells us that:
P(|x-mu|>= k sigma) <= 1/k^2
so P(|x-mu|) >= 2.5 sigma) <= 1/2.5^2 = 0.16
So P(|x-mu| < 2.5 sigma) = 1-0.16 = 0.84.
b) here I presume that we are to assume normality, so we look 2.5 up
in a table of the standard normal distribution to get:
So P(|x-mu| < 2.5 sigma) = 0.9876.
RonL