2 ) Roll of a Die: Suppose you roll a single six-sided die with numbers 1 - 6 printed on the sides. Assume that each side has an equal probability of being rolled. distribution. In the previous problem you created the probability distribution. Calculate the mean of this probability 3 Type yes or no Determine whether the following sequence of trials would result in a binomial probability distribution. a) The National Health Institute checks on 100 people who had a certain type of cancer in the vear b) Calling all your friends until you have 2 people willing to play on your volleyball team. c) Calling 500 people and asking who they voted for in an election. d) Calling 500 people and asking if they voted for a particular candidate in a given election ()I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value Outcomes Value P (x) XP(x) win grand prize 499 1/5000 499/5000 win a 2nd prize 2/5000 win a 3rd prize win a nothing (lose) sum: Expected value in dollars: 5 ) T/F Quiz: Suppose you take a 10 question True or False quiz and you guess on every problem. Find the probability that you only get 2 correct. Round to 3 decimal places. Suppose a certain type of cancer has a 0.76 survival rate for five years. This means that 76% of those diagnosed with this type of cancer have survived at least 5 years (those that die from something else in that time are excluded). Now, suppose you check on 135 people with this type of cancer 5 years after diagnosis and treatment from a particular hospital. Assume the 0.76 survival rate is accurate. In randomly selected groups of 135 people diagnosed with this type of cancer, what is the mean number of survivors at the five-year mark? Round your answer to one decimal place. What is the standard deviation? Round your answer to two decimal places. O= It is estimated that 16.6% of all adults in the U.S. are uninsured. You take a random sample of 250 adults seen by a certain clinic and nd that 50 are uninsured. In such groups of 250 U.S adults, what is the mean number of those that would be uninsured? round to 1 decimal place What is the standard deviation? round to 2 decimal places 0 = Suppose you own a catering company. You hire temporary employees to act as servers from the local college. Not being the most reliable employees, there is an 80% chance that any one server will actually show up for a scheduled event. For a wedding scheduled on a given Saturday you need at least 5 servers. Suppose you schedule 5 employees, what is the probability that all 5 come to work? round to 3 decimal places