A random sample of size 5 is taken from a normal population with mean 2.5 and variance 36. The probability that the sample variance S^2=1/n-1sumi=1^n(Xi-bar X)^2 lies between 27 and 45 is [Given, P(chi4^2ge3)=0.55783 and P(chi4^2le5)=0.71270]

Q35Section I (Objective (Q1–Q80))35 of 80

Statistics — sampling distribution of the sample variance

A random sample of size $5$ is taken from a normal population with mean $2.5$ and variance $36$ . The probability that the sample variance

$S^2=\frac{1}{n-1}\sum_{i=1}^n(X_i-\bar X)^2$

lies between $27$ and $45$ is [Given, $P(\chi_4^2\ge3)=0.55783$ and $P(\chi_4^2\le5)=0.71270$ ]

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