Scenario for Quiz Questions 1 and 2: For a particular house, the number of trick-or-treaters who visit per hour follows a Poisson distribution with a rate of 23 visitors per hour. Let the random variable X count the number of trick-or-treaters who will visit the house during an hour. Quiz Question 1 - Part (a): Compute the probability that during an hour there will be exactly 20 trick-or-treaters who visit the house. Quiz Question 1 - Part (b): Compute the probability that during an hour there will be fewer than 25 trick-or-treaters who visit the house. Quiz Question 2: Using the mean and standard deviation, describe the number of trick-or-treaters who will visit the house during a typical hour. Quiz Question 3: The duration of all hayrides is uniformly distributed between 30 minutes and 55 minutes. Let the random variable X measure the duration of a hayride. Compute the probability that a hayride will last more than 46 minutes. Make sure to sketch and shade the density curve. Quiz Question 4: The diameters of all pumpkins are normally distributed with a mean of 50 cm and a standard deviation of 7 cm. Let the random variable X measure the diameter of a pumpkin. Compute the probability that a pumpkin will have a diameter between 55 cm and 65 cm. Make sure to sketch and shade the density curve