Answer to Question #257723 in Statistics and Probability for Sunil

Question #257723

The probability that the sample man should not differ by population mean by more than a/2 units is 0.95, where σ is the population standard deviation. For the validity of the statement, what should be the size of the sample?

Select one:

a. 18

b. 16

c. 12

d. 20


1
Expert's answer
2021-10-28T11:48:44-0400

(Chebyshev's Theorem) The probability that any random variable XX will assume a value within kk standard deviations of the mean is at least 11/k2.1 — 1/k^2.

That is, P(μkσ<X<μ+kσ)11/k2.P(\mu-k\sigma<X<\mu+k\sigma)\geq1-1/k^2.

Then


11/k2=0.95=>1/k2=1/20=>n=k2=201-1/k^2=0.95=>1/k^2=1/20=>n=k^2=20

d. 20



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