Performance of stock screeners. Investment companies provide their clients with automated tools-called stock screeners to help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Web site, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners. (Note: A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.) Compute the median for the data set. Interpret its value.

$$\begin{array}{lllllllllllll}9.0 & -.1 & -1.6 & 14.6 & 16.0 & 7.7 & 19.9 & 9.8 & 3.2 & 24.8 & 17.6 & 10.7 & 9.1\end{array}$$

To formulate the performance of a multiple-access network, we need a mathematical model. When the number of stations in a network is very large, the Poisson distribution, $p[x] = (e^{−\lambda} \times \lambda^x)/(x!)$, is used. In this formula, p[x] is the probability of generating x number of frames in a period of time and $\lambda$ is the average number of generated frames during the same period of time. Using the Poisson distribution: a. Find the probability that a pure Aloha network generates x number of frames during the vulnerable time. Note that the vulnerable time for this network is two times the frame transmission time (Tfr). b. Find the probability that a slotted Aloha network generates x number of frames during the vulnerable time. Note that the vulnerable time for this network is equal to the frame transmission time (Tfr).

Consider the following key performance indicators, and classify each according to the balanced scorecard perspective it addresses. Choose from financial perspective, customer perspective, internal business perspective, or learning and growth perspective.

a. Number of employee suggestions implemented b. Revenue growth c. Number of on-time deliveries d. Percentage of sales force with access toreal-time inventory levels e. Customer satisfaction ratings f. Number of defects found during manufacturing g. Number of warranty claims h. Return on investment i. Variable cost per unit j. Percentage of market share k. Number of hours of employee training L Number of new products developed m. Yield rate (number of units produced per hour) n. Average repair time o . Employee satisfaction p. Number of repeat customers

Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio. As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected. Washington considers a put option that has a delta of −.65. If the price of the underlying asset decreases by $6, then what is the best estimate of the change in option price?

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions (“Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds,” NHTSA, DOT HS 811 488, June 2011):

$$\begin{matrix} \text{32.1} & \text{30.6} & \text{31.4} & \text{30.4} & \text{31.0} & \text{31.9}\\ \end{matrix}$$

The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using $\alpha=.01$.

A simple solar collector is built by placing a 5-cm-diameter clear plastic tube around a garden hose whose outer diameter is 1.6 cm. The hose is painted black to maximize solar absorption, and some plastic rings are used to keep the spacing between the hose and the clear plastic cover constant. During a clear day, the temperature of the hose is measured to be $65^\circ C,$ while the ambient air temperature is $26^\circ C.$ Determine the rate of heat loss from the water in the hose per meter of its length by natural convection. Also, discuss how the performance of this solar collector can be improved. Evaluate air properties at an average temperature of $50^\circ C$ and 1 atm pressure. Is this a good assumption?

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Calculate the creditor days ratio for Total Oil in $2013$.

Refrigeration units can be rated in "tons." A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton $\left(2000\right.$ pounds $=909 \mathrm{~kg}$ ) of $0^{\circ} \mathrm{C}$ water into $0^{\circ} \mathrm{C}$ ice in one 24-h day. If, on a $35^{\circ} \mathrm{C}$ day, the interior of a house is maintained at $22^{\circ} \mathrm{C}$ by the continuous operation of a 5 -ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $\$ 0.10$ per $\mathrm{kWh}$ and that the unit's coefficient of performance is $15 \%$ that of an ideal refrigerator. $1 \mathrm{kWh}=3.60 \times 10^6 \mathrm{~J}$.

Prof. Hardtack gave four Friday quizzes last semester in his senior tax accounting class. A random sample of 10 student scores is shown for each quiz.

(a) Find the sample mean, standard deviation, and coefficient of variation for each quiz.

(b) How do these data sets differ in terms of center and variability?

(c) Briefly describe and compare student performance on each quiz.

Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99

Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79

Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99

Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98

In order to study the relationship between the amount of sleep a student gets and his or her school performance, a researcher collected data from 120 students. The two-way frequency table shows the number of students who passed and failed an exam and the number of students who got more or less than 6 hours of sleep the night before.

To the nearest percent, find the probability that a student who got less than 6 hours of sleep failed the exam.

For the centrifugal water pump of the earlier problem, plot the pump's performance data: $H$ (ft), bhp (hp), and $\eta_{\text {purp }}$ (percent) as functions of $\dot{V}$ (gpm), using symbols only (no lines). Perform linear least-squares polynomial curve fits for all three parameters, and plot the fitted curves as lines (no symbols) on the same plot. For consistency, use a first-order curve fit for $H$ as a function of $\dot{V}^2$, use a second-order curve fit for bhp as a function of both $\dot{V}$ and $\dot{V}^2$, and use a third-order curve fit for $\eta_{\text {pamp }}$ as a function of $\dot{V}, \dot{V}^2$, and $\dot{V}^3$. List all curve-fitted equations and coefficients (with units) for full credit. Find the BEP of the pump based on the curve-fitted expressions.

Independent random samples are selected from two populations. The data are shown in the following table. Sample 1

$$\begin{matrix} \text{15} & \text{16}\\ \text{10} & \text{13}\\ \text{12} & \text{8}\\ \end{matrix}$$

Sample 2

$$\begin{matrix} \text{5} & \text{9} & \text{5}\\ \text{12} & \text{8} & \text{10}\\ \text{9} & \text{4} & \text{ }\\ \end{matrix}$$

Use the Wilcoxon rank sum test to determine whether the data provide sufficient evidence to indicate a shift in the locations of the probability distributions of the sampled populations. Test, using $\alpha=.05$.

Performance data for a pump are

$$\begin{matrix}\text{H (ft)} & \text{179} & \text{176} & \text{165} & \text{145}\\\text{Q (gpm)} & \text{0} & \text{500} & \text{1000} & \text{1500}\\\text{H (ft)} & \text{119} & \text{84} & \text{43}\\\text{Q (gpm)} & \text{2000} & \text{2500} & \text{3000}\\\end{matrix}$$

Estimate the delivery when the pump is used to move water between two open reservoirs through 1200 ft of 12-in.-diameter commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve if the elevation increase is 50 ft. Determine the gate valve loss coefficient needed to reduce the volume flow rate by half.

The director of graduate admissions at a local university is analyzing the relationship between scores on the Graduate Record Examination (GRE) and subsequent performance in graduate school, as measured by a student's grade point average (GPA). She uses a sample of seven students who graduated within the past five years. A portion of the data is shown in the accompanying table.

$$\begin{array}{|c|c|} \hline \text { CRE } & \text { CPA } \\ \hline 1500 & 3.4 \\ \hline 1400 & 3.5 \\ \hline \vdots & \vdots \\ \hline 800 & 2.7 \\ \hline \end{array}$$

a. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is greater than zero.

b. At the $5 \%$ significance level, are GRE and GPA positively correlated?