A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 23.5 pounds and a standard deviation of 6.9 pounds.

1a) If a sampling distribution is created using samples of the amounts of weight lost by 62 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

1b) If a sampling distribution is created using samples of the amounts of weight lost by 62 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

2) Suppose the horses in a large stable have a mean weight of 1128lbs, and a standard deviation of 58lbs. What is the probability that the mean weight of the sample of horses would be greater than 1136lbs if 37 horses are sampled at random from the stable? Round your answer to four decimal places.

3) Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.9 and a mean diameter of 200 inches. If 78 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 199.8 inches? Round your answer to four decimal places.

4) Suppose cattle in a large herd have a mean weight of 1228lbs and a variance of 8100. What is the probability that the mean weight of the sample of cows would differ from the population mean by less than 9lbs if 115 cows are sampled at random from the herd? Round your answer to four decimal places.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the coins are distinguishable and fair, and that what is observed are the faces uppermost.

Three coins are tossed; the result is at most one tail.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 3.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 11.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 13.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; both numbers are prime. (A positive integer is prime if it is neither 1 nor a product of smaller integers.)

Use the given information to find the indicated probability.

P(A ∪ B) = .8, P(B) = .7, P(A ∩ B) = .4.

Find P(A).

Use the given information to find the indicated probability.

P(A) = .78.

Find P(A').

P(A') =

QUESTION 7

1. Michael surveys children in the special needs class at his church. He wants to know how supportive relationships can influence autistic children's social development. What is the sample?

QUESTION 8

1. When conducting a statistical test, a high p-value indicates

QUESTION 9

1. Which value is used to determine the practical significance of a t-test?

QUESTION 10

1. What is the problem with running multiple t-tests?

QUESTION 11

1. Suppose that an analysis of variance (ANOVA) produces an F statistic with a p-value of .050. What can we conclude based on these results?

QUESTION 12

1. What is the alternate hypothesis of a chi-square test?

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)

6.When comparing the future value of two investments: one that earns 6% p.a. simple interest and the other that earns 6% p.a interest compounding annually, the difference can best be described as:

Select one:

A. the time value of money

B. a pricing convention in money markets

C. compound interest

D. interest on interest

7.A loan for $5,000 is to be repaid by payments of $2,000 after 1 year and $X after 2 years. Interest is at 9%p.a compounding monthly. If we use the monthly periodic interest rate, the time intervals for the timeline should be in:

Select one:

a. Months

b. Years

c. Half-years

d. Quarters

8.Intermediaries, by managing deposits they receive, are able to make loans of a long-term nature whilst satisfying saver's preferences for short-term, liquid claims. This statement is referring to which important attribute of financial intermediation?

Select one:

A. Maturity transformation

B. Credit risk transformation

C. Asset transformation

D. Investment transformation

The effectiveness of antidepressants in treating the eating disorder bulimia was examined in the article “Bulimia Treated with Imipramine: A Placebo-Controlled Double-Blind Study” (American Journal of Psychology [1983]: 554–558). A group of patients diagnosed with bulimia were randomly assigned to one of two treatment groups, one receiving imipramine and the other a placebo. One of the variables recorded was binge frequency. The authors chose to analyze the data using a rank-sum test because it makes no assumption of normality. They stated that “because of the wide range of some measures, such as frequency of binges, the rank sum is more appropriate and somewhat more conservative.” Data on number of binges during one week that are consistent with the findings of the article are given in the following table:

Placebo 8 3 15 3 4 10 6 4

Imipramine 2 1 2 7 3 12 1 5

Do these data strongly suggest that imipramine is effective in reducing the mean number of binges per week? Use a level .05 rank-sum test.

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?