1. At the entrance of Walmart, there is a greeter named Mary who says "Have a nice day" to the customers as they leave the store after shopping. The probability that a customer responds to Mary is 70%. For each of the following scenarios related to Mary the greeter--state the following (note: R.V. means random variable) (1) Define the R.V.--- that means something like, \"Let)( be the number of people who.....\" (2) Define the distribution and parameter(s) of the R.V. (3) Give the support of the R.V. (4) Write the probability statement related to the information being sought. Do NOT calculate the probability. SCENARIOS: 2]) Sophie leaves Walmart and Mary says \"Have a nice day". Find the probability that Sophie does not respond to Mary. b) A family of 5 leaves Walmart after shopping, find the probability that 2 of the family members respond to Mary. Assume that each person's response is independent. c) Maryjust started her work shift at Walma rt. She has said "have a nice day\" to 3 people and received no response. What is the probability that it will take more than 5 people total for Mary to get her first response? cl) What is the probability that Mary will get her 4'[1 response, from the 7th person who walks out? e) The store manager knows that after 5 pm, on average there are 20 customers leaving the store every 30