I am currently working on figuring out sample means that are greater than or less than certain values. I thought I had it down but I am stuck on understanding this problem.
For example:
a population is know to have a Mean of 10 standard deviation .9 a sample size of 75. what is the probability that the same mean is greater than 9.8?
xbar = 9.8
n = 75
s =.9
mean=10
Z = xbar-mean/ standard deviation/ sqr rt of N
9.8-10/ .9/sqr rt 75
= -2
so i look up -2 on the z score chart and its .0028 so that's the "answer".
But the teacher said its .9778 so he did the Z score of 2 not -2 which is what I came up with. & i dont get why?!
The question asks for you to find the probability that X-bar is > 9.8
When you look up z = -2 in most tables, the answer you get is for the probability to the left (less than). So, in your case the answer is going to be 1 - Pr(z = -2) = Pr(z = 2).
So, if you look up z=-2 in the table, the correct answer for X-bar > 9.8 is going to be 1 minus the value from the table (area to the right = greater than).
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