Optional HW 7: Binomial Distributions QO 0:49:52 remaining Page 1: 1 2 3 4 5 7 8 Quiz Information The Fantasy Land Theme Park received many complaints from their customers of extremely long wait times for attractions. As a result, they have decided to limit the number of daily visitors to roughly 2,000 people. Given that not all visitors who purchase tickets in advance show-up, they have decided to sell 5% more than 2,000 tickets each day. They sell the tickets in advance, online, and do not sell any tickets in person on the day-of. As Fantasy Land is very popular, any tickets they offer for sale in advance will sell out. The data in the previous month reveals that out of the 77,340 tickets sold in advance, only 73,473 people actually showed up. Assume last month's percent of people who showed up is reflective of the probably of each person showing up each day. Also assume that each person who shows up act independently of the other visitors (each person has the same probability of showing up). Question 1 (1 point) How many trials, n, are there? n= Question 2 (1 point) If you define "Success" as customer showing up to the theme park, what are the probabilities of Success and Failure for each trial? (based on the last month data) q-= [ ] {answer in decimal form) Question 3 (2 points) Out of the tickets sold, what is the probability of having exactly 2,000 visitors in the theme park per day? (Final answer in decimal form, rounded to 4 decimals) Question 4 (2 points) What is the probability of at most 2,000 visitors per day? (Final answer in decimal form, rounded to 4 decimals) Question 5 (2 points) What is the probability of more than 2,000 visitors per day? (Final answer in decimal form, rounded to 4 decimals) Question 6 (1 point) What is the expected number of visitors showing up in the theme park on a day? Answer in whole number. Question 7 (2 points) What is the probability of having AT LEAST expected number of visitors showing up to the theme park? (Note: expected number of visitors was determined in previous question) (Final answer in decimal form, rounded to 4 decimals) Question 8 (3 points) What is the probability of having more than 5% of the customers who bought the tickets DO NOT show-up to the theme park? (Final answer in decimal form, rounded to 4 decimals)