Question

Assume the sample variances to be continuous measurements. Find the probability that a random sample of 24 observations, from a normal population with variance σ2 = 6, will have a sample variance S2 less than 2.946.

Answer 1

Answer:

Step-by-step explanation:

Hello!

You have a random sample of 24 observations from a normal population with variance δ²= 6.

The distribution of the sample variance is

X²= $\frac{(n-1)S^2}{Sigma^2}$~$X^2_{n-1}$

Using this distribution you can calculate the asked probability:

P(S²<2.946)= P(X²<$\frac{(24-1)2.946}{6}$)= P(X²<11.293)

Now you have to look for the probability in the table of the Chi-square distribution, this particular distribution has n-1= 24-1=23 degrees of freedom, so you have to look for the probability under X²₂₃

P(X²<11.293) = 0.02

I hope this helps!