1. ## Standard Normal Table

Given X~N(µ, 1), find the sample size required to ensure that the probability thatx is within 0.1 of µ is greater than 0.95.

Depending on the table that I used, I got 2 different answers.
i) P(-0.1<
x - µ <0.1) >0.95
2P(Z<0.1/(1/sqrt(n))) -1>0.95
P
(Z<0.1/(1/sqrt(n))) >0.975
0.1/(1/sqrt(n))>1.96
n>384.16
n = 385

ii)
P(-0.1<x - µ <0.1) >0.95
1-2P(Z>0.1/(1/sqrt(n)))>0.95
P(Z>0.1/(1/sqrt(n)))<0.025
0.1/(1/sqrt(n))<1.96
n<384.16
n = 383

I don't understand, where did I do wrong?

2. ## Re: Standard Normal Table

The issue is in the method ii).
You have used $P(Z>.01\sqrt{n})<0.025 \implies 0.1\sqrt{n}<1.96$ which is wrong. It should be $0.1\sqrt{n}>1.96$.
Note that you are looking for upper tail of the distribution in $P(Z>.01\sqrt{n})<0.025$.