Toe Computer Security Institute (CSI) conducts an annual survey of computer crin1e at U.S. businesses. CSI sends survey questionnaires to computer security personnel at all U.S. corporations and government agencies. Toe latest CSI survey was sent by post or email to 5,412 firms, and 351 organizations responded. Forty-one percent of the respondents admitted unauthorized use of computer systems at their firms during the year. (CSI Computer Crime and Security Survey, 2010/2011.) a. Identify the population of interest to CSI. b. Identify the data collection method used by CSI. Are there any potential biases in the method used? c. Describe the variable measured in the CSI survey. Is it quantitative or qualitative? d. What inference can be made from the study result?

Find the inverse Laplace transform of the function. $\frac{Z^{2}}{(z-2)^{3}}$

A and B are subsets of a set S. Prove the following set identities by showing set inclusion in each direction.

$$\left.\begin{array}{l} \text { a. }(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \\ \text { b. }(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \end{array}\right\} \text { De Morgan's laws }$$

c. $A \cup(B \cap A)=A$ d. $\left(A \cap B^{\prime}\right)^{\prime} \cup B=A^{\prime} \cup B$ e. $(A \cap B) \cup\left(A \cap B^{\prime}\right)=A$ f. $[A \cap(B \cup C)]^{\prime}=A^{\prime} \cup\left(B^{\prime} \cap C^{\prime}\right)$

Write the d’Alembert solution for the problem $u_{t t}=c^{2} u_{x x}$ for $-\infty<x<\infty, t>0$ and $u(x, 0)=f(x), u_{t}(x, 0)=g(x)$ for $-\infty<x<\infty$. $c=1, f(x)=x^{2}, g(x)=-x$

Two different box-filling machines are used to fill cereal boxes on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is $\sigma^2= 1$ ounce. Experiments are conducted using both machines with sample sizes of 36 each. The sample averages for machines $A$ and $B$ are $\overline{x}_A = 4.5$ ounces and $\overline{x}_B = 4.7$ ounces. Engineers are surprised that the two sample averages for the filling machines are so different. (a) Use the Central Limit Theorem to determine

$$P( \hat{X}_B − \hat{X}_A \geq 0.2)$$

under the condition that $\mu_A=\mu_B$. (b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different? Explain using your answer in (a).

Use > or < to compare the whole numbers. $74,328 \square 74,238$

Improving SAT scores. Refer to the Chance (Winter 2001) and National Education Longitudinal Survey (NELS) study of 265 students who paid a private tutor to help them improve their SAT scores, Exercise $2.88$ (p. 89). The changes in both the SAT-Mathematics and SAT-Verbal scores for these students are reproduced in the table. Suppose the true population mean change in score on one of the SAT tests for all students who paid a private tutor is 15 . Which of the two tests, SAT-Mathematics or SAT-Verbal, is most likely to have this mean change? Explain.

Perform the elementary row operation or sequence of row operations on A and then produce a matrix $\Omega$ so that $\Omega A$ is the end result.

$$A=\left(\begin{array}{ccc} -4 & 6 & -3 \\ 12 & 4 & -4 \\ 1 & 3 & 0 \end{array}\right)$$

; interchange rows 2 and 3, then add the negative of row 1 to row 2.

Improving SAT scores. The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the Standardized Assessment Test (SAT) scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the changes in both the SAT-Mathematics and SAT-Verbal scores for these students. Repeat part a for the SAT-Verbal score.

Improving SAT scores. Refer to the Chance (Winter 2001) examination of Scholastic Assessment Test (SAT) scores of students who pay a private tutor to help them improve their results, Exercise $2.88$ (p. 89). On the SATMathematics test, these students had a mean score change of $+19$ points, with a standard deviation of 65 points. In a random sample of 100 students who pay a private tutor to help them improve their results, what is the likelihood that the sample mean score change is less than 10 points?

Budget lapsing at army hospitals. Budget lapsing occurs when unspent funds do not carry over from one budgeting period to the next. Refer to the Journal of Management Accounting Research (Vol. 19, 2007) study on budget lapsing at U.S. Army hospitals, Exercise $2.113$ (p. 102). Because budget lapsing often leads to a spike in expenditures at the end of the fiscal year, the researchers recorded expenses per full-time equivalent employee for each in a sample of 1,751 army hospitals. The sample yielded the following summary statistics: $\bar{x}=\$ 6,563$ and $s=\$ 2,484$. Estimate the mean expenses per full-time equivalent employee of all U.S. Army hospitals using a $90 \%$ confidence interval. Interpret the result.

Budget lapsing at army hospitals. Accountants use the term budget lapsing to describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research (Vol. 19, 2007). Data on expenses per full-time equivalent employees for a sample of 1,751 army hospitals yielded the following summary statistics: $\bar{x}=\$ 6,563$, $m=\$ 6,232, s=\$ 2,484, Q_{\mathrm{L}}=\$ 5,309$, and $Q_{\mathrm{U}}=\$ 7,216$. What proportion of the 1,751 army hospitals have expenses between $\$ 5,309$ and $\$ 7,216 ?$

Maximize Z=14x+21y subject to

$$\begin{aligned} 2 x+3 y & \leq 12 \\ x+5 y & \leq 8 \\ x, y & \geq 0 \end{aligned}$$

Find the present value of the given perpetuity. $60,000 per year at the rate of 8% yearly