Question

A random sample of students who rent apartments was taken. What is the probability of getting a sample mean monthly rent that exceeds $660
n=100
Slandered deviation=80
m= 650
x bar= 650

I did 660-650/80= 0.125 but the answer is 0.1056, what am i doing wrong

Answer 1

Since it is exceeds which is greater than
you have to find the find the cumulative proabaility of -0.125

Answer 2

so i look up -0.125 on the Z table

Answer 3

`What is the probability of getting a sample mean monthly rent that exceeds $660`
Translation: \(\mathbb P\left( \bar X > 660 \right) = ?\)
So, \(\mathbb P \left( \frac{(\bar X - 650)}{80/10} > \frac{(660 - 650)}{80/10} \right) = \mathbb P \left( \frac{(\bar X - 650)}{8} > \frac{10}{8} \right) = 1 - \mathbb P \left( \frac{(\bar X - 650)}{8} \le \frac{10}{8} \right) \)
\(= \mathbb P( Normal(0,1) \le 1.25 = 1 - 0.8945\)

That is the complete computation. You must learn to turn an inequality with \(\bar X\) into an inequality with \(\frac{\bar X - m}{\sigma/\sqrt{n}}\).

Answer 4

And use the cool behavior of \(\frac{\bar X - m}{\sigma/\sqrt n}\): it has a standard normal distribution. That's when you can use the table.

Answer 5

question when do I use the T table

Answer 6

When the standard deviation is not given. Then, usually, the statement gives another value: an empirical measure of \(\sigma\), noted \(s\).

Answer 7

You must look carefully in your book or the statement. The "cool fraction" might show a \(n-1\) instead of an \(n\):
\[\frac{\bar X-m}{s/\sqrt{n-1}}\]