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A representing head when a coin is tossed For items 13-15, refer to the scenario and table provided below The number of qualified voters living in the household on a randomly selected Subdivision block is described by the following probability distribution. Number of qualified voter / s, x 1 2 3 4 Probability, P(X) 0.25 0.50 0.15 0.10 13. What is the mean of the probability distribution? 14. What is the standard deviation of the probability distribution? 15. What is the variance of the probability distribution? ACTIVITY 5. PERFORMANCE TASK Directions: Refer to the given situation Mr. Cruz, a Mathematics teacher in University of the North gave a 10 item test to his 10 students. After the test, he checked his students output and found out the scores are as follows: 4, 2, 10, 5, 5, 7, 5, 7, 7,3. Construct probability distribution for the scores obtained by his 10 students and determine the values of the mean, variance and standard distribution of early created probability distribution. Use the back portion as your answer sheet Rubrics for Checking TASK CRITERIA SCORING PERCENTAGE Accuracy of Solution 50% Completeness of needed data and tables 30% Neatness and clarity of work 20% TOTAL 100%A certain municipality found out that the number of infected persons on the new variant of COVID-19 in their 5 barangays are 2, 3, 5, 1, and 6. Suppose that 3 barangays are drawn as sample. 1. What is the mean (u), variance (2) and standard deviation of the population ()? 2. How many different samples of size n =3 can be drawn from the population? 3. List them with their corresponding mean. 4. Construct the sampling distribution of the sample mean. 5. What is the mean (ux) of the sampling distribution of the sample mean? Compare this to the mean of the population. 6. 5. What is the variance of the (ox 2) of the sampling distribution of the sample mean?A. Find the area or region that corresponds to each of the following z values. Sketch and label each curve. Use pencil/pen, ruler and any coloring materials in sketching your curve. 1. below z = 1.41 2. above z = -26 3. Between z = -1.80 and z=2.12 B. Read, analyze and represent the given situation using standard normal distribution. Then answer what is being asked. Show your complete solution. Use the back portion as your answer sheet. Five hundred sixty five patients in a certain hospital were diagnosed, admitted and recovered with Covid- 19 cases. According to hospital staff, the average days of their patients' recovery is 15 days with a standard deviation of 3 days. What is the probability that one patient will recover from Covid-19 virus between 8 - 18 days