Answer:
a)
b)Step-by-step explanation:
Previous concepts
The Chi Square distribution is the distribution of the sum of squared standard normal deviates .
For this case we assume that the sample variance is given by and we select a random sample of size n from a normal population with a population variance
. And we define the following statistic:
And the distribution for this statistic is
For this case we know that n =25 and so then our statistic would be given by:
With 25-1 =24 degrees of freedom.
Solution to the problem
Part a
For this case we want this probability:
And we can multiply the inequality by 4 on both sides and we got:
And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"
Part b
For this case we want this probability:
If we multiply the inequality by 4 on all the terms we got:
And we can find this probability like this:
And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"