I've had a crack at this question however I don't seem to be getting the correct answer and I can't figure out why. I've been given a table of the 'Normal Distribution Function' where the left tail is tabulated for $0\leq x\leq 4$.
Given that $Z\sim N(0,1)$, what is the value of $P(-1.1 < Z < 0.35)$ to 4 decimal places?
My working is as follows: Rearranging the equation first then looking up the values in the given tables. $$P(Z < 0.35) - P(X > -1.1)$$ $$P(Z < 0.35) - P(X < 1.1)$$ $$0.6368 - 0.8643 = -0.2275$$
The given answer for this question is $0.5011$.
Could someone please explain where I'm falling short and how to correctly solve this question?
You want $\Pr(Z\lt 0.35)-\Pr(Z\le -1.1)$.
The table does not have direct information about $\Pr(Z\le a)$ for negative $a$.
But by symmetry we have $\Pr(Z\le -1.1)=\Pr(Z\ge 1.1)$.
Note that $\Pr(Z\ge 1.1)=1-\Pr(Z\lt 1.1)$.
Now you have all the needed components.