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

Consider the region bounded by the graphs of  and

Which of the following correctly describes the pathophysiology of Addison’s disease?

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