Calculate the mean and standard deviation of the discrete probability distribution (round to 3 decimal places when necessary): X 0 5 10 15 20 25 30 35 40 P(x) 0.08 0.1 0.11 0.13 0.12 0.11 0.12 0.11 0.12 Mean: 0.000 Standard Deviation: 0.000Out of all patients being admitted to a particular ward of a hospital, approximately 11% 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, '12 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 |east4 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 to 4 signicant digits c. Expected # of Private Room Requests = 0 Round to nearest whole number d. Range of Expected Requests = O to 0 Round to nearest whole number Question 4 of 6 The following contingency table details the sex and age distribution of the patients currently registered at a family physician's medical practice. If the doctor sees 18 patients per day, use the binomial formula and the information contained in the table to answer the question: AGE SEX Under 20 20-39 40-59 60-79 80 or over TOTAL Male 5.6% 12.8% 18.4% 14.4% 3.6% 54.8% Female 2.8% 9.6% 13.2% 10.4% 9.2% 45.2% TOTAL 8.4% 22.4% 31.6% 24.8% 12.8% 100.0% What is the probability that exactly 1 of the patients seen in a day are females aged 20 39? Round to 4 signicant drgits. 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. Out of 22 nurse practitioners who are on call on a given day, 4 are sick. If two on-call nurse practitioners are called in based on a random selection, determine the probability distribution for the number of sick nurse practitioners who are called in. P (x) 0.6623 0.3116 0.0259 Round probabilities to 4 decimal places E (X) = 0.36 Round to 2 decimal places Var (X) = 0.28 Round to 2 decimal places