Question

A random variable X is normally distributed. Suppose we obtain a random sample of 11 elements from the population. Further assume that the population variance is 100. Find the probability that the sample variance is at least 48.6.

Answer 1

The random variable x is normally distributed.

The sample size is n=11

Population variance is = 100

Calculate the probability that the sample varance is at least 48.6

P(s² 48.6) = 1- P (s²48.6)

= 1 - P

= 1- P

= 1-P(X²4.86)(From chi-square table)

= 1-0.09967

=0.90