Suppose the number X of tornadoes observed in a particular region during a 1-year period has a Poisson distribution with λ = 9. (a) Compute P(X<=5).
(b) Compute P(6<= X<= 9)
(c) Compute P(10<= X)
(d) What is the probability that the observed number of tornadoes exceeds the expected number by more than 1 standard deviation?

Which interval for the graphed function contains the local maximum? [–3, –2] [–2, 0] [0, 2] [2, 4]

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?

Determine whether the quadrilateral below is a parallelogram. justify/explain your answer (this means back it up! give specific information that supports your decision. writing just "yes" or "no" will result in no credit.)