A random sample of size

n = 21 is taken from a Normal distribution with unknown mean μ

and known variance

= 23.6. The sample mean is 1.3.

(a) Write down the 100(1 − a)% two–sided confidence interval for μ when a= 0.05.

(b) If the length of the confidence interval is not exceed the value 2, what is the sample size that should be taken to ensure this?

(c) Describe the changes to the confidence interval if varianceis unknown and replaced by the

sample variance.

I struggle with part b), and part c)

Any help would be great, thanks