You play a carnival game where you have to throw a ball into a barrel to win a $20 prize. You will play a maximum of three times, but walk away if you win. If it costs $4 to play and you have a 5% chance of making a throw, find the expected value and standard deviation of your "winnings" (cost included).

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?