A friend tosses a coin 100 times and gets 62 heads…

Step 1. Mean and spread. $\mu = 50$ heads and $\sigma = \sqrt{25} = 5$ heads.

Step 2. How far. $\dfrac{62 - 50}{5} = 2.4$ standard deviations above the mean, outside the usual range.

Step 3. The exact tail. Adding $\binom{100}{k}/2^{100}$ for $k = 62$ to $100$ gives about $0.0105$.

What it means. A fair coin gives $62$ or more heads only about once in $100$ runs of $100$ tosses. That is not proof, but it is a reason to doubt the coin. The last chapter of this book turns this idea into a test.