Question

Assume the sample variances random sample of 25 observations, from a normal population with variance σ2 = 6, will have a sample variance S2 greater than 9.1;

Answer 1

To find the probability that the sample variance of a random sample will be greater than a given value, we can use the chi-square distribution.

Step-by-step explanation:

The question is asking about the probability that the sample variance of a random sample of 25 observations from a normal population with variance σ2 = 6 will be greater than 9.1. In order to solve this, we need to find the distribution of the sample variance under the given conditions.

First, we need to calculate the sample standard deviation using the formula:

S = sqrt(S2) = sqrt(9.1) = 3.01

Next, we can use the chi-square distribution to find the probability that the sample variance is greater than 9.1. We use the formula:

P(S2 > 9.1) = P((n-1) * S2 / σ2 > (n-1) * 9.1 / 6) = P((24 * S2) / 6 > 24 * 9.1 / 6) = P(X > 36)

Using the chi-square distribution table or a calculator, we can find the probability that X is greater than 36. This will give us the probability that the sample variance is greater than 9.1.