I need your help solving this problem. Please help me by answering and showing explanations.

Problem 1. (30 points). You decide to talce an internship this summer. Unfortunately, you decide to intern with your shady brother-inlaw's company, Engineer Nick's.1 Engineer Nick's is a low-budget consulting rm which offers civil engineering services at steeply discounted prices. Over the summer, you are assigned to produce concrete blocks for strength testing along with several other interns. During the next 32 days, you count how many interns show up for work (including you) and the number of blocks you are able to produce each day, producing the following table of probabilities between the two values: While the rst two planks in your platform fail to get much traction, the third gains a considerable amount of support. Indeed, you conduct a survey of 12 students who reveal the total amount they have spent on transcriptrelated fees: Number of months Number of interns 1 2 3 1/32 3/32 0/ 32 3/32 5/32 4/32 0/ 32 7/32 5/ 32 0/32 ? 3/32 Blocks produced #WMO (a) (5) What is the missing value in the table? (b) (5) The company expects daily production of at least one block per intern who showed up. What is the probability that this goal is achieved? (c) (10) What is the correlation coeicient between the number of interns who show up and the number of blocks produced? (d) (10) Each intern is paid $72 per day worked, and each produced block leads to a net gain of $144. What is the expected daily prot for the company? (Assume prot is \"net gain\" minus wages paid to interns.)