Central Limit Theorem

The mean is \(\displaystyle np=100(1/2)=50\)

The standard deviation is \(\displaystyle \sqrt{npq}=\sqrt{100(1/2)(1/2)}=5\)

The given formula in the solution is how the values in a z table are found.

The limits of integration indicate z scores from 0 to 2 standard deviations above the mean. The mean being at 0.

\(\displaystyle z=\frac{50-50}{5}=0\)

\(\displaystyle z=\frac{60-50}{5}=2\)

See now how they got those integration limits?.

0 is at the mean and z=2 corresponds to 2 standard deviations above the mean.

The CLT tells us that 0 to 2 SD above the mean is about how much area under the normal curve?.

I bet it's close to what they gave.

The given integral does not have an elementary antiderivative. That is, it is not easily done by hand. Use tech to get the solution or some numerical method

if you must deal with it. This is why we use a z table, They are already calculated.
 
Well, of course, the probability of heads each flip is 1/2. To get the mean, I wasn't sure if I could just multiply that by the total number of flips.

I was going to ask where you got np, but now I see it earlier in the notes in the derivation of the CLS. He has the standard deviation = np(1 - p). What is q?

Oops. I really should read the notes more thoroughly. I'm ready for this semester to be over.
 
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