Which of the following questions would help uncover value assumptions?

Instructions: You have 3 hours (8PM – 11PM) to complete the exam.  This is a closed book and closed notes exam. Only a physical scientific calculator is allowed. No graphing calculators, electronic devices, books, notes, or other reference materials are permitted during the exam. You may only use a pen or pencil and blank scratch paper. Write all answers clearly in the space provided and show all necessary work to receive full credit. If you need additional space or prefer to write your solutions on separate sheets, you may do so. In that case, clearly label each sheet with your name and the corresponding question number. After completing the questions, scan your solutions and upload them to Canvas as a SINGLE .pdf file. You may use your phone to scan your work. Then, either share the file with your computer or email it to yourself in order to upload it. Ensure that all pages are legible, properly ordered, and clearly labeled with your name. Now you can start. Exam 2 – make up.pdf

A stamping machine produces can tops whose diameters are normally distributed with a standard deviation of 0.01 inch. At what “normal” (mean) diameter should the machine be set so that no more than 5% of the can tops produced have diameters exceeding 3 inches? (10 points)

X 0 1 2 3 4 p(X) 0.07 0.15 0.45 0.25 0.08   Given the probability distribution of X, estimate the following: a. Mean (4 points) b. Variance (4 points) c. Standard deviation (2 points)

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of the penetration of the point. Suppose the Rockwell Hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness? (5 points) b. If the acceptable range of hardness is (70-c, 70+c), for what value of c would 95% of all specimens have acceptable hardness? (5 points)

Upon reviewing the recent use of conference rooms at an engineering consulting firm, an industrial engineer determined the following probability distribution for the number of requests for a conference room: X (number of rooms needed on a given day) 0 1 2 3 4 p(X) 0.07 0.15 0.45 0.25 0.08   If there are only two conference rooms available in the building: a. What is the probability that the number of requests will exceed the number of rooms available? (3 points) b. What is the probability that the two conference rooms will not be fully utilized? (3 points) c. How many additional conference rooms are required so that the probability of denying a request is not more than 0.10? (4 points)

If a random variable X has the log-normal distribution with average of -1 and standard deviation of 2: a. Find the mean and standard deviation of X. (3 points) b. Find the probability that the random variable X will take on a value between 3.2 and 8.4 (3 points) c. Find the probability that the random variable X will take on a value greater than 5 (4 points)

Compute the area of the enclosed region bounded by the graphs of the equations and

A force of 20 lb stretches a spring from a natural length of 7 inches to a length of 12 inches. How much work was performed in stretching the spring to this length?

Find the length of the graph for