A branch manager of a brokerage company is concerned with the number of undesirable trades made by her sales staff. A trade is considered undesirable if there is an error on the trade ticket. Trades with errors are canceled and resubmitted. The cost of correcting errors is billed to the brokerage company. The branch manager wants to know whether the proportion of undesirable trades is in a state of statistical control so she can plan the next step in a quality improvement process. Data were collected for a 30 -day period and stored in Trade.

a. Construct a control chart for these data.

b. Is the process in control? Explain.

c. Based on the results of (a) and (b), what should the manager do next to improve the process?

One of the buffer systems used to control the pH of blood involves the equilibrium between $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$and $\mathrm{HPO}_4{ }^{2-}$. The $\mathrm{p} K_{\mathrm{a}}$ for $\mathrm{H}_2 \mathrm{PO}_4^{-}$is 7.21. (a) Write the Henderson-Hasselbalch equation for this buffer system. (b) What $\mathrm{HPO}_4{ }^{2-}$ to $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$ratio is needed to maintain the optimum blood pH of 7.40?

A chemical production process uses water-cooling to carefully control the temperature of the system so that the correct products are obtained from the resulting chemical reaction. The temperature of the system must be maintained at a temperature of 120 degrees Fahrenheit. A technician suspects that the average temperature is different from 120 degrees Fahrenheit and checks the process by taking temperature readings at 12 randomly selected times over a 4-hour period. Here are the data:

120.1 124.2 122.4 124.4 120.8 121.4

121.8 119.6 120.2 121.5 118.7 122.0

A 95% confidence interval for $\mu$ is 120.335 degrees Fahrenheit to 122.515 degrees Fahrenheit. Explain how this interval is consistent with the test in the previous part.

Managers at some companies face an ongoing systems development crisis: IS departments develop systems that businesses cannot or will not use. At the heart of the problem is a "great divide" that separates the world of business and the world of IS. Few departments seem able or ready to cross this gap.

One reason for the crisis is that many companies are looking for ways to improve existing, out-of-date systems or to build new ones. Another is the widespread use of PC-based systems that have spawned high user expectations that IS departments are not meeting. Users seek more powerful applications than are available on many older systems.

The costs of the great divide can be devastating. An East Coast chemical company spent over $1 million on a budgeting and control system that was never used. The systems department's expertise was technical excellence, not budgets. As a result, the new system completely missed the mark when it came to meeting business needs. A Midwestern bank used an expensive computer-aided software engineering (CASE) tool to develop a system that users ignored because there had been no design planning. A senior analyst for the bank said, "They built the system right; but unfortunately they didn't build the right system."

d. Who plays the most vital role in the effective development of the system?

Red Valve Co. of Carnegie, Pennsylvania, makes a control pinch valve that provides accurate, repeatable control of abrasive and corrosive slurries, outlasting gate, plug, ball, and even satellite coated valves. How much can the company afford to spend now on new equipment in lieu of spending $75,000 four years from now? The company’s rate of return is 12% per year.

Describe some optimal control problems in your major field or in another area of interest to you. How difficult would it be to find the optimal controls?

Derive a control volume form of the second law of thermo-dynamics. Suggest some practical uses for your relation in analyzing real fluid flows.

Use the sample size formula to decide on a sample size large enough to avoid constructing a p-chart with a negative lower control limit.

b. $p_0=0.05$

In a control system, an accelerometer consists of a $4.70-\mathrm{g}$ object sliding on a horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of $0.800 \mathrm{~g}$, the object is to assume a location $0.500 \mathrm{~cm}$ away from its equilibrium position. Find the force constant required for the spring.

In the following, name the term defined or answer the question.

A Six Sigma process that is running at the center of its control limits would expect this defect rate.

Select the letter of the item that best defines the italicized word in the sentence.

He must control his rage and not be so bellicose.

a. quarrelsome b. act of resistance

Note that some of the lines of the poem run on as if they’re out of control; they seem too long. Why might the poet have chosen to write this way?

Look at Table 24.4. What is easier to control—toxic chemicals leaching out of landfills or toxic chemicals in surface runoff? Defend your answer

To control an agricultural pest called the medfly (Mediterranean fruit fly), $N$ sterilized male flies are released into the general fly population every day. If $s$ is the proportion of these sterilized flies that survive a given day, then $Ns^k$ will survive for $k$ days. If $s=$ 0.9 and 10,000 sterilized males are needed to control the medfly population in a given area, how many should be released every day?