(4 points) The number of pedestrians using a busy crosswalk can be modeled by a Poisson distribution with A = 56.1746 pedestrians per hour. Suppose you randomly pick 53 different one-hour time frames during which you observe the crosswalk. Let X be the number of pedestrians you observe in each of these 53 times frames. Use this information to answer the following questions. a. Describe the distribution of X and the distribution of the sample mean 2K. Round all values to at least five decimals if necessary pedestrians and a standard deviation (IX of The distribution of X is ? V with a mean x of pedestrians. The distribution of Y is. 7 V with a mean u)? of pedestrians and a standard deviation 0" of _ X pedestrians. b. What is the probability that the average number of pedestrians using the crosswalk per hour in this sample will be between 54.2 and 57.24? Answer: Round to at least five decimals if necessary 0. What is the probability that the number of pedestrians using the crosswalk in a single one-hour time frame will be more than 50? Answer: Round to at least five decimals if necessary d. 63% of the time, the average number of pedestrians using the crosswalk for a sample of 53 one-hour time frames will be at most how many? Answer: pedestrians. Hound to at least five decimals if necessary