The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute. (a) What is the probability distribution for x, the number of visits per minute? p(x) = X (b) What is the probability that the number of visits per minute is less than or equal to 10? (Round your answer to three decimal places.) x (c) What is the probability that the number of visits per minute is greater than 15? (Round your answer to three decimal places.)

The probability that a randomly selected teenager watched a rented video at least once during a week was 0.69. What is the probability that at least 7 teenagers in a group of 9 watched a rented movie at least once last week? (Round your answer to four decimal places.) P(X ≥ 7) =

Today, the waves are crashing onto the beach every 4.4 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.4 seconds. Round to 4 decimal places where possible.   The probability that the wave will crash onto the beach between 1.2 and 2.1 seconds after the person arrives is P(1.2 < x < 2.1) =  The probability that it will take longer than 3.28 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.28) =  Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3 and 3.7 seconds for the wave to crash onto the shoreline.  62% of the time a person will wait at least how long before the wave crashes in?  seconds. Find the minimum for the upper quartile.  seconds. Hint:

The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide