Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level is above 130 milligrams per deciliter (mg/dl) one hour after a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 115 mg/dl and σ = 14 mg/dl. *I would really appreciate a step by step to solve these problems*

Let X = Sheila's measured glucose level one hour after a sugary drink

(a) P(X > 130) = (Use 3 decimal places)

Suppose measurements are made on 3 separate days and the mean result is compared with the criterion 130 mg/dl.

(b) P(X > 130) = (Use 3 decimal places)

(c) What sample mean blood glucose level is higher than 95% of all other sample mean blood glucose levels? Hint: this requires a backward Normal calculation. (Use 2 decimal places)

A bag contains 3 red marbles, 2 green ones, 1 lavender one, 3 yellows, and 3 orange marbles. HINT [See Example 7.]

How many sets of five marbles include at least two red ones?
sets

Write a C program for a PIC18F4321 microcontroller to convert eight LM-34 temperature sensors, which are connecte4d to AN0 to AN7, and display on a display consisting of two 7-segment displays. Use a three-bit switch to select one of the eight sensors to display.

CASE:

In re The Walt Disney Co. Derivative Litigation

907 A.2d 693 (Del. Ch. 2005)

JACOBS, Justice:

[The Walt Disney Company hired Ovitz as its executive president and as a board member for five years after lengthy compensation negotiations. The negotiations regarding Ovitz’s compensation were conducted predominantly by Eisner and two of the members of the compensation committee (a four-member panel). The terms of Ovitz’s compensation were then presented to the full board. In a meeting lasting around one hour, where a variety of topics were discussed, the board approved Ovitz’s compensation after reviewing only a term sheet rather than the full contract. Ovitz’s time at Disney was tumultuous and short-lived.]…In December 1996, only fourteen months after he commenced employment, Ovitz was terminated without cause, resulting in a severance payout to Ovitz valued at approximately $ 130 million. [Disney shareholders then filed derivative actions on behalf of Disney against Ovitz and the directors of Disney at the time of the events complained of (the “Disney defendants”), claiming that the $130 million severance payout was the product of fiduciary duty and contractual breaches by Ovitz and of breaches of fiduciary duty by the Disney defendants and a waste of assets. The Chancellor found in favor of the defendants. The plaintiff appealed.]

We next turn to the claims of error that relate to the Disney defendants. Those claims are subdivisible into two groups: (A) claims arising out of the approval of the OEA [Ovitz employment agreement] and of Ovitz’s election as President; and (B) claims arising out of the NFT [nonfault termination] severance payment to Ovitz upon his termination. We address separately those two categories and the issues that they generate.…

…[The due care] argument is best understood against the backdrop of the presumptions that cloak director action being reviewed under the business judgment standard. Our law presumes that “in making a business decision the directors of a corporation acted on an informed basis, in good faith, and in the honest belief that the action taken was in the best interests of the company.” Those presumptions can be rebutted if the plaintiff shows that the directors breached their fiduciary duty of care or of loyalty or acted in bad faith. If that is shown, the burden then shifts to the director defendants to demonstrate that the challenged act or transaction was entirely fair to the corporation and its shareholders.…

The appellants’ first claim is that the Chancellor erroneously (i) failed to make a “threshold determination” of gross negligence, and (ii) “conflated” the appellants’ burden to rebut the business judgment presumptions, with an analysis of whether the directors’ conduct fell within the 8 Del. C. § 102(b)(7) provision that precludes exculpation of directors from monetary liability “for acts or omissions not in good faith.” The argument runs as follows: Emerald Partners v. Berlin required the Chancellor first to determine whether the business judgment rule presumptions were rebutted based upon a showing that the board violated its duty of care, i.e., acted with gross negligence. If gross negligence were established, the burden would shift to the directors to establish that the OEA was entirely fair. Only if the directors failed to meet that burden could the trial court then address the directors’ Section 102(b)(7) exculpation defense, including the statutory exception for acts not in good faith.

This argument lacks merit. To make the argument the appellants must ignore the distinction between (i) a determination of bad faith for the threshold purpose of rebutting the business judgment rule presumptions, and (ii) a bad faith determination for purposes of evaluating the availability of charter-authorized exculpation from monetary damage liability after liability has been established. Our law clearly permits a judicial assessment of director good faith for that former purpose. Nothing in Emerald Partners requires the Court of Chancery to consider only evidence of lack of due care (i.e. gross negligence) in determining whether the business judgment rule presumptions have been rebutted.…

The appellants argue that the Disney directors breached their duty of care by failing to inform themselves of all material information reasonably available with respect to Ovitz’s employment agreement.…[but the] only properly reviewable action of the entire board was its decision to elect Ovitz as Disney’s President. In that context the sole issue, as the Chancellor properly held, is “whether [the remaining members of the old board] properly exercised their business judgment and acted in accordance with their fiduciary duties when they elected Ovitz to the Company’s presidency.” The Chancellor determined that in electing Ovitz, the directors were informed of all information reasonably available and, thus, were not grossly negligent. We agree.

…[The court turns to good faith.] The Court of Chancery held that the business judgment rule presumptions protected the decisions of the compensation committee and the remaining Disney directors, not only because they had acted with due care but also because they had not acted in bad faith. That latter ruling, the appellants claim, was reversible error because the Chancellor formulated and then applied an incorrect definition of bad faith.

…Their argument runs as follows: under the Chancellor’s 2003 definition of bad faith, the directors must have “consciously and intentionally disregarded their responsibilities, adopting a ‘we don’t care about the risks’ attitude concerning a material corporate decision.” Under the 2003 formulation, appellants say, “directors violate their duty of good faith if they are making material decisions without adequate information and without adequate deliberation[,]” but under the 2005 post-trial definition, bad faith requires proof of a subjective bad motive or intent. This definitional change, it is claimed, was procedurally prejudicial because appellants relied on the 2003 definition in presenting their evidence of bad faith at the trial.…

Second, the appellants claim that the Chancellor’s post-trial definition of bad faith is erroneous substantively. They argue that the 2003 formulation was (and is) the correct definition, because it is “logically tied to board decision-making under the duty of care.” The post-trial formulation, on the other hand, “wrongly incorporated substantive elements regarding the rationality of the decisions under review rather than being constrained, as in a due care analysis, to strictly procedural criteria.” We conclude that both arguments must fail.

The appellants’ first argument—that there is a real, significant difference between the Chancellor’s pre-trial and post-trial definitions of bad faith—is plainly wrong. We perceive no substantive difference between the Court of Chancery’s 2003 definition of bad faith—a “conscious and intentional disregard [of] responsibilities, adopting a we don’t care about the risks’ attitude…”—and its 2005 post-trial definition—an “intentional dereliction of duty, a conscious disregard for one’s responsibilities.” Both formulations express the same concept, although in slightly different language.

The most telling evidence that there is no substantive difference between the two formulations is that the appellants are forced to contrive a difference. Appellants assert that under the 2003 formulation, “directors violate their duty of good faith if they are making material decisions without adequate information and without adequate deliberation.” For that ipse dixit they cite no legal authority. That comes as no surprise because their verbal effort to collapse the duty to act in good faith into the duty to act with due care, is not unlike putting a rabbit into the proverbial hat and then blaming the trial judge for making the insertion.

…The precise question is whether the Chancellor’s articulated standard for bad faith corporate fiduciary conduct—intentional dereliction of duty, a conscious disregard for one’s responsibilities—is legally correct. In approaching that question, we note that the Chancellor characterized that definition as “an appropriate (although not the only) standard for determining whether fiduciaries have acted in good faith.” That observation is accurate and helpful, because as a matter of simple logic, at least three different categories of fiduciary behavior are candidates for the “bad faith” pejorative label.

The first category involves so-called “subjective bad faith,” that is, fiduciary conduct motivated by an actual intent to do harm. That such conduct constitutes classic, quintessential bad faith is a proposition so well accepted in the liturgy of fiduciary law that it borders on axiomatic.…The second category of conduct, which is at the opposite end of the spectrum, involves lack of due care—that is, fiduciary action taken solely by reason of gross negligence and without any malevolent intent. In this case, appellants assert claims of gross negligence to establish breaches not only of director due care but also of the directors’ duty to act in good faith. Although the Chancellor found, and we agree, that the appellants failed to establish gross negligence, to afford guidance we address the issue of whether gross negligence (including a failure to inform one’s self of available material facts), without more, can also constitute bad faith. The answer is clearly no.

…”issues of good faith are (to a certain degree) inseparably and necessarily intertwined with the duties of care and loyalty.…” But, in the pragmatic, conduct-regulating legal realm which calls for more precise conceptual line drawing, the answer is that grossly negligent conduct, without more, does not and cannot constitute a breach of the fiduciary duty to act in good faith. The conduct that is the subject of due care may overlap with the conduct that comes within the rubric of good faith in a psychological sense, but from a legal standpoint those duties are and must remain quite distinct.…

The Delaware General Assembly has addressed the distinction between bad faith and a failure to exercise due care (i.e., gross negligence) in two separate contexts. The first is Section 102(b)(7) of the DGCL, which authorizes Delaware corporations, by a provision in the certificate of incorporation, to exculpate their directors from monetary damage liability for a breach of the duty of care. That exculpatory provision affords significant protection to directors of Delaware corporations. The statute carves out several exceptions, however, including most relevantly, “for acts or omissions not in good faith.…” Thus, a corporation can exculpate its directors from monetary liability for a breach of the duty of care, but not for conduct that is not in good faith. To adopt a definition of bad faith that would cause a violation of the duty of care automatically to become an act or omission “not in good faith,” would eviscerate the protections accorded to directors by the General Assembly’s adoption of Section 102(b)(7).

A second legislative recognition of the distinction between fiduciary conduct that is grossly negligent and conduct that is not in good faith, is Delaware’s indemnification statute, found at 8 Del. C. § 145. To oversimplify, subsections (a) and (b) of that statute permit a corporation to indemnify (inter alia) any person who is or was a director, officer, employee or agent of the corporation against expenses…where (among other things): (i) that person is, was, or is threatened to be made a party to that action, suit or proceeding, and (ii) that person “acted in good faith and in a manner the person reasonably believed to be in or not opposed to the best interests of the corporation.…” Thus, under Delaware statutory law a director or officer of a corporation can be indemnified for liability (and litigation expenses) incurred by reason of a violation of the duty of care, but not for a violation of the duty to act in good faith.

QUESTION:   
i. How did the court view the plaintiff’s argument that the Chancellor had developed two different types of bad faith? Why?
ii. What two statutory provisions has the Delaware General Assembly passed that address the distinction between bad faith and a failure to exercise due care (i.e., gross negligence)? Why are they important?

Concert Nation] Concert Nation, INC. is a nationwide promoter of rock concerts. The president of
the company wants to develop a model to estimate the revenue of a major concert event at large venues
(such as Ford Field, Madison Square Gardens) for planning marketing strategies. The company has
collected revenue data of 32 recent large concert events. For each concert, they have also recorded the
attendance, the number of concession stands in the venue, and the Billboard chart of the artist in the
week of each event. This data is available in “Tickets”. They have two potential models that could
explain the revenue. The two competing models are:

Model A: ??????? = ?? + ???????????? + ???????????? + ??????????? + ?0123?

Model B: ??????? = ?? + ???????????? + ??????????? + ?012?

Run regression on both models. Use only the regression outputs of the two models and the original data
to answer questions 1 to 7 below.
1. [1 pt] Let’s consider the model A first. What does the result of F-test indicate?
(a) The p-value of F-test is 100.83. Thus, the model does not significantly explain the revenue.
(b) The p-value of F-test is close to zero. Thus, all independent variables in the regression model are
statistically significant.
(c) The p-value of F-test is close to zero. This indicates that at least some independent variables in the
regression model significantly explain the revenue.
(d) This indicates weak evidence of a linear relationship, because the p-value is very low.
2
2. [1 pt] If we use model A for prediction, what is the point estimate for the revenue of a concert that has
attendance of 50,000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking?
(a) $3.145 M
(b) $2.851 M
(c) $3.252 M
(d) $340K
3. [1 pt] What is an approximate 95% prediction interval for the concert listed in the previous question?
(a) [$2.757M, $3.533M]
(b) [$2.463M, $3.239M]
(c) [$2.368M, $3.922M]
(d) [$2.074M, $3.628M]
4. [1 pt] Which of the following statement is correct?
(a) The estimated slope for the attendance is only $59.2. This means that, when keeping everything
else the same, the revenue does not depend much on the attendance.
(b) The t-statistic associated with the slope for the attendance variable is 16.9. This means that there is
too much noise to determine if the slope is definitely positive.
(c) The p-value for the concession variable is 0.933. This means that the number of concession stands
is not a statistically significant variable to determine the revenue.
(d) The p-value for the concession variable is 0.933. This means that the number of concession stands
is a statistically significant variable to determine the revenue.
5. [1 pt] Is it appropriate to use model A as a final model to estimate the revenue of a concert?
(a) Yes. All independent variables are statistically significant.
(b) Yes, because the analysis indicates a linear relationship between revenue and attendance.
(c) No, because not all independent variables are statistically important. Thus, revision is necessary.
(d) No, because some of the slopes were negative. Thus, revision is necessary.
3
6. [1 pt] Now, consider model B. According to model B, what is a point estimate for a concert that has
attendance of 50000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking?
(a) $3.147M
(b) $2.839M
(c) $7.139M
(d) $13.637M
7. [1 pt] Based on the regression outputs, which model would you consider more suitable for predicting the
revenue between the two models– Model A and Model B?
(a) Model A is more suitable, because it has a higher ?2, lower standard error of the estimates
(??), and lower F-test p-value.
(b) Model A is more suitable because the fraction of SST accounted for by the residuals is higher than
for model B.
(c) Model B is more suitable, because, while both models have similar ?2 and F-test p-value, model B
has lower standard error of the estimates (??) and all independent variables are statistically
significant.
(d) Model B is more suitable, because the slope coefficient is larger in magnitude.

Match each example to the type of bias that would result

1. An experiment consists of drawing two marbles from a box containing red, yellow, and green marbles. One event in the sample space is RR. What are all of the events in the sample space? (Note: order matters) (3)

2. In a certain large population, 46% of households have a total annual income of over $70,000. A simple random sample is taken of four of these households. What is the probability that more than 2 of the households in the survey have an annual income of over $70,000?                                                                (8)

3. Which would you expect to have a higher standard deviation: data scores that are spread out or data scores that are close together?   
4. In a survey of U.S. households, 588 had home computers while 722 did not. Use this sample to estimate the probability of a household having a home computer.

1. Home Security Systems is studying the time utilization of its sales force. A random sample of 40 sales calls showed that the representatives spend an average of ẍ = 44 minutes on the road with a standard deviation of s = 6 minutes for each sales call.

1. Create a line showing the mean and values for 4 standard deviations above and 4 standard deviations below the mean.                                                                                                                                                (2)

2. Use Chebyshev’s Theorem to find the values between which we can expect at least 89% of the data to fall.                                                                                                                                                                       (2)

3. At least what percent of the data can we expect to fall between 38 and 50 minutes using the Empirical Rule?                                                                                                                                                        (2)

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had a distribution where the possible values of X are 1, 2, 3, 4 with the corresponding probabilities of 0.2, 0.4, 0.3, and 0.1. Use this information to answer questions 20-23 below.

2. Does the above data form a probability distribution? Create the distribution and explain why or why not.(5)

3. Using the above data, what is the probability that a randomly chosen subject completes at least three puzzles in the five-minute period while listening to soothing music?                                                                   (2)

4. Using the above data, the mean µ of X is what? Show work.                                                                             (3)
5. Using the above data (on previous page), the standard deviation σ of X is what? Show work.                      (4)

1. Why would we use the 10-90 percentile range?                                                                                                  +2

2. A data set has a range of 348. Use the range rule of thumb to determine the standard deviation.        +1

A batch of 26 light bulbs includes 5 that are defective. Two light bulbs are randomly selected. If the random variable, X, represents the number of defective light bulbs which can be selected, what values can X have?                

Exercise 16-44 Comprehensive Cost Variance Analysis (LO 16-5, 6)

NSF Lube is a fast-growing chain of oil-change stores. The following data are available for last year’s services:

NSF Lube performed 467,700 oil changes last year. It had budgeted 435,000 oil changes, averaging 8 minutes each.

Standard variable labor and support costs per oil change were as follows:

Direct oil specialist services: 8 minutes at $30 per hour $ 4.00

Variable support staff and overhead: 10.5 minutes at $20 per hour 3.5

Fixed overhead costs: Annual budget $1,039,000

Fixed overhead is applied at the rate of $3.90 per oil change.

Actual oil change costs:

Direct oil specialist services: 467,700 changes averaging 11 minutes at $34 per hour $ 2,915,330

Variable support staff and overhead: 0.22 labor-hours at $15 per hour × 467,700 changes 1,543,410

Fixed overhead 1,425,000

a. Prepare a cost variance analysis for each variable cost for last year.

b. Prepare a fixed overhead cost variance analysis

I know the answer for b is:

Price Variance: $386,000 U

Production Volume Variance: $785,030 F

Fixed Overhead Cost Variance: $399,030 F

......But I can't figure out A: how to get the Price Variance, Efficiency Variance or the total variance for both the oil specialist and the variable overhead.

Any help would be appreciated.

The marketing division of Family FunTime Mini Golf is wanting to gather information about the spending habits of its visitors. It polls visitors as they leave and gathers information about the amount of money spent at the course. A sample with 40 families and the amounts they spent can be found in the Excel table I have provided below. Please answer all questions using complete sentences.

1. Using Excel’s PivotTable feature, organize the data into a frequency distribution, using 7 classes and 15 as the lower limit of the first class. Copy your table below. (You can do a straight copy/paste from Excel, it will transfer the table over.) What class interval did you need to select? Explain.
2. Where do the data tend to cluster? Describe the distribution in the context of the problem.
3. Determine the relative frequency distribution using your PivotTable in Excel. Copy your table below.
4. Determine the cumulative percent frequency distribution using your PivotTable in Excel. Copy your table below.

The marketing division of Family FunTime Mini Golf is wanting to gather information about the spending habits of its visitors. It polls visitors as they leave and gathers information about the amount of money spent at the course. A sample with 40 families and the amounts they spent can be found in the Excel table I have provided below. Please answer all questions using complete sentences.

1. Using Excel’s PivotTable feature, organize the data into a frequency distribution, using 7 classes and 15 as the lower limit of the first class. Copy your table below. (You can do a straight copy/paste from Excel, it will transfer the table over.) What class interval did you need to select? Explain.
2. Where do the data tend to cluster? Describe the distribution in the context of the problem.
3. Determine the relative frequency distribution using your PivotTable in Excel. Copy your table below.

4. Determine the cumulative percent frequency distribution using your PivotTable in Excel. Copy your table below.