We have a problem which gives us the $\mu = 170.035$ we also have our $\sigma = 1.122$ Now the question asks Using the Normal approximation we get that the central region that contains 95% of the distribution of the sample average is of the form 170.035 ± z · 1.122. The value of z is?
I found the value that is greater than 95% of the graph using qnorm which gave me 171.8805 I then subtracted the $\mu$ value and divided by $\sigma$ to find the z value which was 1.645 (rounded). The answer stated it was 1.959964 but this value is for regions 0.975 I am a bit puzzled at how the got that answer
If you want the 95% of the population in a gaussian you have two tails, so you need to consider the popultaion between 2.5% and 97.5%