A very good poker player is expected to earn \($1\) per hand in \($100\)/\($200\) Texas Hold’em. The standard deviation is approximately \($32\).

(a) What is the probability a very good poker player earns a profit (more than \($0\)) after playing 50 hands in \($100\)/\($200\) Texas Hold’em?

(b) What is the probability a very good poker player loses (earns less than \($0\)) after playing 100 hands in \($100\)/\($200\) Texas Hold’em?

(c) What proportion of the time can a very good poker player expect to earn at least \($500\) after playing 100 hands in \($100\)/\($200\) Texas Hold’em? \($500\) after 100 hands is a mean of \($5\) per hand.

(d) Would it be unusual for a very good poker player to lose at least \($1000\) after playing 100 hands in \($100\)/\($200\) Texas Hold’em?

(e) Suppose twenty hands are played per hour. What is the probability that a very good poker player earns a profit during a twenty-four hour marathon session?