Calculate the mean and standard deviation of the discrete probability distribution. Mean: 0.000 Round to three decimal places if necessary Standard Deviation: 0.000 Round to three decimal places if necessary Analyze the scenario and complete the following: i. Complete the discrete probability distribution for the given variable. ii. Calculate the expected value and variance of the discrete probability distribution. The value of a ticket in a small hospital lottery, in which 2,000 tickets are sold, with 1 grand prize of $3,500, 5 first prizes of $400, 40 second prizes of $150, and 55 third prizes of $40. Round probabilities to 4 decimal places E (X) = $0.00 Round to 2 decimal places Var (X) = 0.00 Round to 2 decimal places Use the binomial formula to calculate the probability of the indicated event to 3 significant digits: n = 10, p = 0.21, P(4 s X s 6) P(4 s X s 6) = 0Out of all patients being admitted to a particular ward of a hospital, approximately 28% choose a private room (at an additional cost) versus a semi-private or ward room. However, since there are a limited number of private rooms available, not all patients can have their requests honoured. Today, 17 patients are admitted to this ward, but there are only 3 private rooms available. a. What is the probability that exactly three patients will request a private room? b. What is the probability that a patient will not have his/her request for a private room honoured (i.e., at least 4 patients will request private rooms)? c. What is the expected number of patients that will request a private room today? d. Using the Range Rule of Thumb, what is the approximate range of the number of patients that will request a private room today? a. P(Exactly 3) = 0 Round to 4 signicant digits b. P(Public Room) = 0 Round [0 4 Signicant digits c. Expected # of Private Room Requests = 0 Round to nearest whole number d. Range of Expected Requests = 0 to 0 Round to nearest whole number A veterinarian performs 40 operations to neuter/spay pets in a month. What is the probability that exactly half of the animals are male and half are female? 0 Round to 3 significant digits