A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. One in three said they expected to burn out in the job in the near future. Thirty-four percent said they thought seriously about quitting their job last year because of work-place stress. Fifty-three percent said they were required to work more than 40 hours a week very often or somewhat often. a. Suppose a random sample of 10 American workers is selected.What is the probability that more than seven of them say job stress caused frequent health problems? What is the expected number of workers who say job stress caused frequent health problems? b. Suppose a random sample of 15 American workers is selected. What is the expected number of these sampled workers who say they will burn out in the near future? What is the probability that none of the workers say they will burn out in the near future? c. Suppose a sample of seven workers is selected randomly. What is the probability that all seven say they are asked very often or somewhat often to work more than 40 hours a week? If this outcome actually happened, what might you conclude?
In: Statistics and Probability
1. [25 marks] Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution, determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗ = 1,360.
Now consider a more general objective function, c1x1 + c2x2. Perform a sensitivity analysis to determine when the current solution remains optimal in the following cases:
(i) both c1 and c2 may vary;
(ii) c2 = 50, c1 may vary;
(iii) c1 = 40, c2 may vary
Suppose the RHS of the second constraint increases by an amount ∆b. (It is now 120 + ∆b.) Solve the two equations for x1 and x2 in terms of ∆b, and hence determine its shadow price.
In: Advanced Math
Based on the information given below, calculate (a) the portfolio’s return in the last 12 months in the USD, (b) its return in the AUD, and (c) the standard deviation of the portfolio return. Provide all the workings (use up to 3 decimal places).
Your stock portfolio consists of two American companies; Alphabet and GM. You are living in Australia and those shares are purchased in the USD. During the last 12 months, Alphabet’s stock went up by 20%, while GM went up by 3%. During the same period, the USD went down by 2% against the AUD. Assume that you have invested 40% of your money to Alphabet and allocated 60% of your money to GM. Furthermore, assume that the standard deviations of stock returns are 7% for Alphabet and 4% for GM, and the correlation coefficient between the two stock is 0.2
In: Finance
Based on the information given below, calculate (a) the portfolio’s return in the last 12 months in the USD, (b) its return in the AUD, and (c) the standard deviation of the portfolio return. Provide all the workings (use up to 3 decimal places). Your stock portfolio consists of two American companies; Alphabet and GM. You are living in Australia and those shares are purchased in the USD. During the last 12 months, Alphabet’s stock went up by 20%, while GM went up by 3%. During the same period, the USD went down by 2% against the AUD. Assume that you have invested 40% of your money to Alphabet and allocated 60% of your money to GM. Furthermore, assume that the standard deviations of stock returns are 7% for Alphabet and 4% for GM, and the correlation coefficient between the two stock is 0.2
In: Finance
An LC circuit is built with a 10 mH inductor and an 12.0 pF capacitor. The capacitor voltage has its maximum value of 40 V at t=0s.
Part A
How long is it until the capacitor is first fully discharged?
Express your answer with the appropriate units. (t=?)
Part B
What is the inductor current at that time?
Express your answer with the appropriate units.(I=?)
In: Physics
A. BNSF Railway operates dual-track intermodal routes between major ports and cities, like two lanes on a highway.
B. Designing a bluetooth system for a phone that is too fast for the latest model.
C. Despite thousands of designs and materials, eyeglasses are basically a frame with two folding arms that go over each ear, and a pair of lenses.
D. The car dealer has 100 cars on the lot. 3000 more are in teh distribution center near the ship channel, and a virtually limitless capacity is available from the factory in Europe.
E. UPS Readies Freezer Farms to Store Virus Vaccine When Approved
F. My phone has a battery but I carry an external rechargeable one for long trips.
G. If you assume people vote loyally to their chosen political party, then straight ticket voting allows you to select your party's candidate for every office in an election with a single click.
H. A car at stage 12 at the assembly plant is having its tires installed while the seats are placed in another vehicle in stage 11.
match with 8 great ideas in computer architecture
In: Computer Science
A. BNSF Railway operates dual-track intermodal routes between major ports and cities, like two lanes on a highway.
B. Designing a bluetooth system for a phone that is too fast for the latest model.
C. Despite thousands of designs and materials, eyeglasses are basically a frame with two folding arms that go over each ear, and a pair of lenses.
D. The car dealer has 100 cars on the lot. 3000 more are in teh distribution center near the ship channel, and a virtually limitless capacity is available from the factory in Europe.
E. UPS Readies Freezer Farms to Store Virus Vaccine When Approved
F. My phone has a battery but I carry an external rechargeable one for long trips.
G. If you assume people vote loyally to their chosen political party, then straight ticket voting allows you to select your party's candidate for every office in an election with a single click.
H. A car at stage 12 at the assembly plant is having its tires installed while the seats are placed in another vehicle in stage 11.
match with 8 great ideas in computer architecture
In: Computer Science
In large corporations, an "intimidator" is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him or herself talk. Let x1 be a random variable representing productive hours per week lost by peer employees of an intimidator.
| x1: | 7 | 2 | 6 | 3 | 2 | 5 | 2 |
A "stressor" is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let x2 be a random variable representing productive hours per week lost by peer employees of a stressor.
| x2: | 3 | 3 | 9 | 8 | 6 | 2 | 5 | 8 |
Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.)
| x1 | = 1 |
| s1 | = 2 |
| x2 | = 3 |
| s2 | = 4 |
(a) Assuming the variables x1 and
x2 are independent, do the data indicate that
the population mean time lost due to stressors is greater than the
population mean time lost due to intimidators? Use a 5% level of
significance. (Assume the population distributions of time lost due
to intimidators and time lost due to stressors are each
mound-shaped and symmetric.)(i) What is the level of
significance?
5
State the null and alternate hypotheses.
H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 > μ2H0: μ1 < μ2; H1: μ1 = μ2
(ii) What sampling distribution will you use? What assumptions are
you making?
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? Compute the
corresponding z or t value as appropriate. (Test
the difference μ1 − μ2. Do
not use rounded values. Round your final answer to three decimal
places.)
8
(iii) Find (or estimate) the P-value.
P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005
Sketch the sampling distribution and show the area corresponding to
the P-value.
(iv) Based on your answers in parts (i)−(iii), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level α?
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
(v) Interpret your conclusion in the context of the
application.
Fail to reject the null hypothesis, there is sufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators. Reject the null hypothesis, there is insufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators. Reject the null hypothesis, there is sufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators. Fail to reject the null hypothesis, there is insufficient evidence that the mean time lost due to stressors is greater than the mean time lost due to intimidators.
(b) Find a 90% confidence interval for
μ1 − μ2.
(Round your answers to two decimal places.)
| lower limit | 13 |
| upper limit | 14 |
Explain the meaning of the confidence interval in the context of
the problem.
Because the interval contains only positive numbers, this indicates that at the 90% confidence level, the population mean time lost due to "stressors" is less than the population mean time lost due to "intimidators." Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, we cannot say that there is any difference in time lost due to "intimidators" and "stressors." Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, there is a difference in time lost due to "intimidators" and "stressors." Because the interval contains only negative numbers, this indicates that at the 90% confidence level, the population mean time lost due to "stressors" is greater than the population mean time lost due to "intimidators."
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In: Statistics and Probability
The following tables list the ages of female and male actors when they starred in their award-winning Best Actor performances. (A graphing calculator is recommended.)
Ages of Best Female Actor Award Recipients
|
50 37 25 33 43 59 74 73 78 26 45 53 43 47 26 32 64 45 75 41 44 21 60 73 76 77 57 79 71 71 74 28 74 55 |
Ages of Best Male Actor Award Recipients
|
46 69 56 55 33 41 53 58 50 69 51 55 55 33 67 47 45 34 59 60 40 50 37 37 74 42 74 53 75 62 73 36 41 59 |
(a) Find the mean and the sample standard deviation of the ages of the female recipients. Round each result to the nearest tenth.
| mean | yr |
| sample standard deviation | yr |
(b) Find the mean and the sample standard deviation of the
ages of the male recipients. Round each result to the nearest
tenth.
| mean | yr |
| sample standard deviation | yr |
(c) Which of the two data sets has the larger mean?
female actors or male actors
Which of the two data sets has the larger standard deviation?
female actors or male actors
In: Statistics and Probability
) Let X ={35, 45, 39, 41, 41, 44, 46, 48, 49, 34, 12, 50, 20, 38, 40}(a.) Insert X into R. (a.) Find the mean of X. (b.) Depict X in a boxplot. (NOTE: This question should be answered entirely using code for R.)
In: Statistics and Probability