Question

In a certain​ distribution, the mean is 100 with a standard deviation of 4. Use​ Chebyshev's Theorem to tell the probability that a number lies between 92 and 108

The probability a number lies between

92

and

108

is at least

Answer 1

Answer:

(Upper - ) / = (108 - 100) / 4 = 2

( - lower) / = (100 - 92) / 4 = 2

In this case k = 2 , the probability that X is within 4 standard deviations of the mean at least

Pr(|X - | < k) 1 - 1/k2

Pr(92 < X < 108) 1 - 1/22

= 4 - 1 /4

= 3/4

= 0.75

Probability = 0.75

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