# Math Help - confidence intervals

1. ## confidence intervals

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?

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

2. since you know $\sigma$ the interval is

$\bar X\pm (1.96)(\sigma/\sqrt{n})$

3. solve for n where

$1.96\sqrt{23.6}/\sqrt{n}<2$....

$(1.96)^2(23.6)/4

any number bigger than $(1.96)^2(23.6)/4$

will work, but most people want the smallest integer that exceeds this value.