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Question 4 (10 marks) Marks a. The following table shows the number of posts on social media per day (x) of 20 random users and their corresponding probabilities. The lowest and highest posts per day are zero and ve, respectively. Number of posts on social media per day (x) i. Complete the table above. [2] ii. What is the probability that a user posts, at most, 3 times? [1] iii. Compute the expected number of posts per day. [1] iv. Compute the standard deviation of the number of posts per day. [1] Question 4 (continued) Marks b. In a box of floppy disks, 90% will work. If a sample of 10 floppy disks is selected at random: i. What is the probability that 7 of them will work? [1] ii. What is the probability that 2 of them will not work? [1] iii. Compute the expected number of the disks that will work from the sample. [1] iv . Compute the standard deviation for the number of the disks that will work from the sample. [1] C. A marketing company gets, on average, 20 orders per 500 calls. If a company calls 500 people, find the probability of getting 12 orders. Assume that the number of orders received by the telemarketing company is Poisson distributed. [1]