Answer to Question #257723 in Statistics and Probability for Sunil

Question

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

Answer 1

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

That is, $P(\mu-k\sigma<X<\mu+k\sigma)\geq1-1/k^2.$

Then

$$1-1/k^2=0.95=>1/k^2=1/20=>n=k^2=20$$

d. 20