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Page 3 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 left behind Probability 0.35 0.12 0. 1 0. 13 Find the missing probability and answer the following questions. a) How many forgotten items should the next class expect to find? b) What is the standard deviation for this distribution? 6) (Beyond the Basics) 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? 7) A man Invests $400 in a tech stock. The probability that the stock will rise tomorrow is 0.06. If it rises, his NET gain Is $8000, but if it falls, he loses his original Investment ($400). Construct the probability distribution and calculate the expected gain in this transaction? 8) You play a coin game in which you win $1.50 if the coin shows heads and you lose $2 If it shows tails. Let the random variable be the amount you win in one game. Construct the discrete probability distribution for the random variable and calculate E(X). 9) Let the random variable X represent the number of boys in a family with five children. Construct a table describing the probability distribution, and then find the mean and standard deviation