A random sample of sizen = 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?

Help with part two is needed, if you could possibly go through the question it would be very appreciated, Thanks.