Ohn Jay is a major league pitcher. He pitches like a robot, that is he pitches the same way to each batter. There is a .56 probability that the first ball he pitches to a batter is a strike. (first-pitch strike). This is independent from batter to batter. Let X equal the number of first-pitch strikes John Jay throws in a game where he pitches to 15 batters. Let Y equal the number of batters he pitches to until he throws his 2nd first-pitch strike. (could be more than 15)

a. What is the probability X=13?
b. What is the standard deviation of X?
c. What is the probability that X > 10?
d. What is the probability that X ≥ 12?
e. What is the probability that Y = 3?
f. What is the probability that Y = 2?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

The domain of a function can be represented by which one of the following options? o a. a set of output values o b. a set of f(x) values o c. a set of input values o d. a set of both input and output values

Which equation can be used to measure the density of water in a spherical water tank? let w represent the number of water particles within the region.