1] Verify whether the following are Probability Distributions 2]An ice cream store has anywhere from 2 to 8 avors of ice cream every day. The probability function for the number of avors is given below : Number ofavors Corresponding probabilities a) Verify mat this is a probability distribution . b) Draw histogram 3] The number of cartons of cookies that each Girl Scout sells has the probabilities given below : Number of cartoons (2;) a) Is this a probability distribution '? b] What is the average number of cartons a girl scout sells ? c) What is the amount of variation '2' Find the range of usual values . 4] A orist buys 60 roses on Valentine's Day . The number of roses he sells has the following probability distribution Find the expected value for the above probability distribution ,and explain your answer . 5} The number of items left behind by students in a lecture hall after a large lecture has the following probability distribution Number of items le behind Probability Complete the above table and answer the following questions (a) How many forgotten items should the next class expect to nd ? (b) What is the standard deviation for this function ? 6] A woman wants to adopt four pets , either cats or dogs , or both , but she is not sure how many of each . a) Construct the probability distribution for the number of cats she can adopt . [Use a tree diagram and assume equal probability for adopting a cat or a dog.) b] What are the mean and standard deviation for the number of cats she adopts