A game of chance offers the following odds and payoffs. Each play of the game costs $$100,$ so the net profit per play is the payoff less $$100.$

Probability Payoff Net Profit

$0\mathrm{.}10$ $$600$ $$500$

$0\mathrm{.}501000$

$0\mathrm{.}400100$

a$-1.$ What is the expected cash payoff?

Note: Round your answer to the nearest whole dollar amount.

a$-2.$ What is the expected rate of return?

Note: Enter your answer as a percent rounded to the nearest whole number.

b$-1.$What is the variance of the expected returns?

Note: In the calculation, use the percentage values, not the decimal values for the rates of return. Do not round intermediate calculations. Round your answer to the nearest whole number.

b$-2.$hat is the standard deviation of the expected returns?

Note: Enter your answer as a percent rounded to $2$ decimal places.