The scores of applicants taking an aptitude test necessary f

The scores of applicants taking an aptitude test necessary for entrance exams follow a normal distribution. A random sample of 25 scores is taken.

A) what is probability that the sample variance is up to 50% larger than the population variance?

B)What is the probability that the population variance is up to 50% larger than the sample variance?

C)There is a 95% probability that the population variance is smaller than the simple variance to an amount of __% of the sample variance?

D) There is a 90% probability that the population variance is larger than the simple variance up to an amount of __% of the sample variance?

Solution

without knowing the population/ sample parameter, this question can\'t be answered.We have to know, which parameters are known..like sample mean or population mean........sample variance or popltn variance and then we can decide what we have to estimate and then we can calculate probability..

If we consider sample variance = a and estimate populaion variance from this.then popltn variance = a/25....
a is always greater than a/25...
so,A) ans=0 B) ans = 1..C) 95% and D) 10%...

But again..this is too intuitive!