The waiting times X and Y (in minutes) of two clients A and B who are standing in line at two different check outs in the supermarket are modeled as independent, exponential random variables with parameter 1.
(a) Find the cumulative distribution function of the random variable M :=min{X,Y} where min{x,y} is just the smaller value of the two numbers.
(b) Find the probability density function of M. Do you recognize the socalled probability law or probability distribution of the random variable M?
(c) What is the probability that both clients wait more than 2 minutes?
In: Math
7. An assembly line at a plant produces exactly 10000 widgets a day. Suppose that approximately 1 out of every 2000 fails a standards test and is thrown out. What is the probability that there will be 10 or more widgets thrown out on a given day?
8. There are 100 green balloons and 150 red balloons in a bag. Suppose we extract 10 balloons from the bag. (a) What is the exact probability that five of the balloons will be green? (b) Use Binomial Approximation to find the probability that exactly five of the balloons will be green. (c) Use Binomial Approximation to find the probability that no more than four of the balloons are green
In: Math
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541 g and a standard deviation of 0.0517g. A sample of these candies came from a package containing 440 candies and the package label stated that the net weight is 375.6 ( If every package has 440 candies, the mean weight of the candies must exceed 374 / 440= 0.8536 g for the net contents to weigh at least 375.6 g)g.)
a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8536 g
The probability is.........(Round to four decimal places as needed.)
b. If 440 candies are randomly selected, find the probability that their mean weight is at least 0.8536 g
The probability that a sample of 440 candies will have a mean of 0.8536 g or greater is........... (Round to four decimal places as needed.)
c.Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label?
..............because the probability of getting a sample mean of 0.8536 g or greater when 440 candies are selected.................exceptionally small.
440440
candies are randomly selected, find the probability that their mean weight is at least
0.85360.8536
g.The probability that a sample of
440440
candies will have a mean of
0.85360.8536
g or greater is
nothing.
(Round to four decimal places as needed.)
c. Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label?
▼
No,
Yes,
because the probability of getting a sample mean of
0.85360.8536
g or greater when
440440
candies are selected
▼
is
is not
exceptionally small.
In: Statistics and Probability
1.Assume that X is a hypergeometric random variable with N = 15, S = 5, and n = 5. Calculate the following probabilities. (Round your answers to 4 decimal places.)
| a | p(x=1) | |
| b | p(x=5) | |
| c | p(x≥2) |
2. Consider the following discrete probability
distribution.
| x | −20 | −5 | 10 | 20 |
| P(X = x) | 0.44 | 0.18 | 0.09 | |
a. Complete the probability distribution.
(Round your answer to 2 decimal places.)
b. What is the probability that the random
variable X is positive? (Round your answer to 2
decimal places.)
c. What is the probability that the random
variable X is greater than −15? (Round your answer
to 2 decimal places.)
d. What is the probability that the random
variable X is less than 20? (Round your answer to
2 decimal places.)
3. An analyst has developed the following probability
distribution for the rate of return for a common stock.
| Scenario | Probability | Rate of Return | ||
| 1 | 0.23 | −10 | % | |
| 2 | 0.42 | 3 | % | |
| 3 | 0.35 | 16 | % | |
a. Calculate the expected rate of return. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)
b. Calculate the variance and the standard
deviation of this probability distribution. (Use the
percentage values for your calculations (for example 10% not 0.10).
Round intermediate calculations to at least 4 decimal places. Enter
your answers as a percentage rounded to 2 decimal
places.)
In: Statistics and Probability
Consider the following data for the patients taking the drug (Ascorbic Acid).
| Placebo | Drug | Sum | |
| Cold | 36 | 87 | 123 |
| NoCold | 224 | 333 | 557 |
| Sum | 260 | 420 | 680 |
What is the probability that a patient has No Cold? Is this a marginal or joint probability?
a) 0.18 marginal
b) 0.62 marginal
c) 0.82 marginal
d) 0.82 joint
e) 0.86 joint
Question 15
What is the probability that a patient is taking Placebo and has No Cold? Is this a marginal or joint probability?
a) 0.86 joint
b) 0.33 joint
c) 0.33 marginal
d) 0.82 marginal
e) 0.82 joint
Question 16
What is the probability that a patient is taking Placebo or has No Cold and identify the correct formula for this kind of probability?
a) 0.92 F5c
b) 0.87 F5a
c) 0.33 F5c
d) 0.92 F5b
e) 0.87 F5b
Question 17
Find conditional probability P(No Cold | taking the drug), P(No Cold | taking Placebo), P(taking drug | No Cold) and identify the correct formula for this kind of probability?
a) 0.49, 0.33, 0.82 F5ef
b) 0.18, 0.62, 0.82 F5c
c) 0.6, 0.71, 0.79, F5ef
d) 0.79, 0.86, 0.6 F5g
e) 0.79, 0.86, 0.6 F5ef
Question 18
Based on answers to previous questions the row and column variables are ________ (a) independent (b) dependent (c) marginal (d) conditional (e) joint
a) marginal
b) joint
c) dependent
d) independent
e) conditional
In: Statistics and Probability
The Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table are obtained for four counties in one region. (Give all answers to four decimal places.)
| County | Race/Ethnicity | ||||
| Caucasian | Hispanic | Black | Asian | American Indian |
|
| Monterey | 163,000 | 140,000 | 25,000 | 39,000 | 5,000 |
| San Luis Obispo | 190,000 | 38,000 | 7,000 | 9,000 | 3,000 |
| Santa Barbara | 230,000 | 121,000 | 12,000 | 24,000 | 5,000 |
| Ventura | 430,000 | 231,000 | 19,000 | 50,000 | 8,000 |
C. If one Hispanic person is selected at random from this region, what is the estimated probability that the selected individual is from Ventura?
(e) If one person is selected at random from this region, what
is the estimated probability that the person is either Asian or
from San Luis Obispo County?
(f) If one person is selected at random from this region, what is
the estimated probability that the person is Asian or from San Luis
Obispo County but not both?
(g) If two people are selected at random from this region, what is
the estimated probability that both are Caucasians?
(h) If two people are selected at random from this region, what is
the estimated probability that neither is Caucasian?
(i) If two people are selected at random from this region, what is
the estimated probability that exactly one is a Caucasian?
(j) If two people are selected at random from this region, what is
the estimated probability that both are residents of the same
county?
(k) If two people are selected at random from this region, what is
the estimated probability that both are from different
racial/ethnic groups?
In: Statistics and Probability
*Practice Exercise 8–1: Analyzing Mixed Costs
The Metropolis Health System has a system-wide training course for nurse aides. The course requires a packet of materials that MHS calls the training pack. Due to turnover and because the course is system-wide, there is a monthly demand for new packs. In addition the local community college also obtains the training packs used in their credit courses from MHS.
The Education Coordinator needs to know how much of the cost is fixed and how much of the cost is variable for these training packs. She decides to use the high-low method of computation.
Required
Using the monthly utilization information presented below, find the fixed and variable portion of costs through the high-low method.
Number of
Month
Training
Packs
Cost
January 1,000 $6,200
February 200 1,820
March 250 2,350
April 400 3,440
May 700 4,900
June 300 2,730
July 150 1,470
August 100 1,010
September 1,100 7,150
October 300 2,850
November 250 2,300
December 100 1,010
Solution to Practice Exercise 8–1
Step 1. Find the highest volume of 1,100 packs at a cost of $7,150 in September and the lowest volume of 100 packs at a cost of $1,010 in August.
Step 2. Compute the variable rate per pack as:
Training
#
of
Packs
Pack Cost
Highest volume 1,100 $7,150
Lowest volume 100 1,010
__________________
Difference 1,000 $6,140
Step 3. Divide the difference in cost ($6,140) by the difference in # of packs (1,000) to arrive at the variable cost rate:
$6,140 divided by 1,000 meals = $6.14 per pack.
Step 4. Compute the fixed overhead rates as follows:
At the highest level:
Total cost $7,150
Less: Variable portion
[1,100 packs × $6.14 @] (6,754)
______
Fixed Portion of Cost $396
At the lowest level:
Total cost $1,010
Less: Variable portion
[100 packs × $6.14 @] (614)
______
Fixed Portion of Cost $396
Proof totals: $396 fixed portion at both levels.
*Assignment Exercise 8–1: Analyzing Mixed Costs
The Education Coordinator decides that the Community College packs may be unduly influencing the high-low computation. She decides to re-run the results omitting the Community College volume.
Required
Using the monthly utilization information presented below, and omitting the Community College training packs, find the fixed and variable portion of costs through the high-low method. Note that the college only acquires packs in three months of the year: January, May, and September. These dates coincide with the start dates of their semesters and summer school.
The reason the Education Coordinator needs to know how much of the cost is fixed is because she is supposed to collect the appropriate variable cost from the Community College for their packs. For her purposes, which computation do you believe is better? Why?
|
Month |
Total Number of Training Packs |
Total Cost |
Community College Number Packs |
Community College Cost |
|
January |
1,000 |
$6,200 |
200 |
$1,240 |
|
February |
200 |
1,820 |
||
|
March |
250 |
2,350 |
||
|
April |
400 |
3,440 |
||
|
May |
700 |
4,900 |
300 |
2,100 |
|
June |
300 |
2,730 |
||
|
July |
150 |
1,470 |
||
|
August |
100 |
1,010 |
||
|
September |
1,100 |
7,150 |
300 |
1,950 |
|
October |
300 |
2,850 |
||
|
November |
250 |
2,300 |
||
|
December |
100 |
1,010 |
Assignment Exercise 8–2: Calculating the Contribution Margin
The Mental Health program for the Community Center has just completed its fiscal year end. The Program Director determines that his program has revenue for the year of $1,210,000. He believes his variable expense amounts to $205,000 and he knows his fixed expense amounts to $1,100,000.
Required
Compute the contribution margin for the Community Center Mental Health program.
What does the result tell you about the program?
Assignment Exercise 8–3: Calculating the PV Ratio and the CVP Ratio
Use the same assumptions for the Greenside Clinic as in Practice Exercise 7–2. One more assumption will be added: the Clinic had 35,000 visits.
Required
In addition to the contribution margin figures already computed, now compute the PV Ratio (also known as CM Ratio).
Add another column to your worksheet and compute the clinic’s per-visit revenue and costs.
Create a Cost-Volume-Profit chart. Refer to the chapter text along with Figure 8–6.
In: Accounting
53.
Blaser Corporation had $1,035,000 in invested assets, sales of $1,266,000, operating income amounting to $203,000 , and a desired minimum return on investment of 14%. The return on investment for Blaser Corporation is
Round the percentage to one decimal place.
a.19.6%
b.23.5%
c.12.8%
d.16.0%
52.
ABC Corporation has three support departments with the following costs and cost drivers:
| Support Department | Cost | Cost Driver |
| Graphics Production | $200,000 | number of copies made |
| Accounting | 500,000 | number of invoices processed |
| Personnel | 400,000 | number of employees |
ABC has three operating divisions, Micro, Macro, and Super. Their revenue, cost, and activity information are as follows:
| Micro | Macro | Super | |
| Revenues | $700,000 | $850,000 | $650,000 |
| Direct operating expenses | 50,000 | 70,000 | 100,000 |
| Number of copies made | 20,000 | 30,000 | 50,000 |
| Number of invoices processed | 700 | 800 | 500 |
| Number of employees | 130 | 145 | 125 |
The operating income of the Super Division after all support department allocations will be
a.$325,000
b.$550,000
c.$200,000
d.$300,000
51.
ABC Corporation has three support departments with the following costs and cost drivers:
| Support Department | Cost | Cost Driver |
| Graphics Production | $200,000 | number of copies made |
| Accounting | 500,000 | number of invoices processed |
| Personnel | 400,000 | number of employees |
ABC has three operating divisions, Micro, Macro, and Super. Their revenue, cost, and activity information are as follows:
| Micro | Macro | Super | |
| Revenues | $700,000 | $850,000 | $650,000 |
| Direct operating expenses | 50,000 | 70,000 | 100,000 |
| Number of copies made | 20,000 | 30,000 | 50,000 |
| Number of invoices processed | 700 | 800 | 500 |
| Number of employees | 130 | 145 | 125 |
The support department cost that will be allocated to the Super Division is
a.$100,000
b.$550,000
c.$350,000
d.$125,000
50.
ABC Corporation has three support departments with the following costs and cost drivers:
| Support Department | Cost | Cost Driver |
| Graphics Production | $200,000 | number of copies made |
| Accounting | 500,000 | number of invoices processed |
| Personnel | 400,000 | number of employees |
ABC has three operating divisions, Micro, Macro, and Super. Their revenue, cost, and activity information are as follows:
| Micro | Macro | Super | |
| Revenues | $700,000 | $850,000 | $650,000 |
| Direct operating expenses | 50,000 | 70,000 | 100,000 |
| Number of copies made | 20,000 | 30,000 | 50,000 |
| Number of invoices processed | 700 | 800 | 500 |
| Number of employees | 130 | 145 | 125 |
The support department cost that will be allocated to the Macro Division is
a.$130,000
b.$175,000
c.$305,000
d.$405,000
49.
ABC Corporation has three support departments with the following costs and cost drivers:
| Support Department | Cost | Cost Driver |
| Graphics Production | $200,000 | number of copies made |
| Accounting | 500,000 | number of invoices processed |
| Personnel | 400,000 | number of employees |
ABC has three operating divisions, Micro, Macro, and Super. Their revenue, cost, and activity information are as follows:
| Micro | Macro | Super | |
| Revenues | $700,000 | $850,000 | $650,000 |
| Direct operating expenses | 50,000 | 70,000 | 100,000 |
| Number of copies made | 20,000 | 30,000 | 50,000 |
| Number of invoices processed | 700 | 800 | 500 |
| Number of employees | 130 | 145 | 125 |
The support department allocation rate for the Personnel Department is
a.$3,200
b.$3,077
c.$2,758
d.$1,000
48.
ABC Corporation has three support departments with the following costs and cost drivers:
| Support Department | Cost | Cost Driver |
| Graphics Production | $200,000 | number of copies made |
| Accounting | 500,000 | number of invoices processed |
| Personnel | 400,000 | number of employees |
ABC has three operating divisions, Micro, Macro, and Super. Their revenue, cost, and activity information are as follows:
| Micro | Macro | Super | |
| Revenues | $700,000 | $850,000 | $650,000 |
| Direct operating expenses | 50,000 | 70,000 | 100,000 |
| Number of copies made | 20,000 | 30,000 | 50,000 |
| Number of invoices processed | 700 | 800 | 500 |
| Number of employees | 130 | 145 | 125 |
The support department allocation rate for Graphics Production is
a.$6.66
b.$2.00
c.$0.50
d.$10.00
47.
Which of the following is a measure of a manager's performance working in a profit center?
a.the divisional income statements
b.a balance sheet
c.a budget performance report
d.the return on investment and residual income measures
46.
Responsibility accounting reports for profit centers will include
a.costs only
b.revenues, expenses, and operating income or loss
c.expenses and fixed assets
d.revenues only
45.
The following data are taken from the management accounting reports of Dulcimer Co.:
| Division A | Division B | Division C | |
| Operating income | $1,900,000 | $1,450,000 | $1,450,000 |
| Total support department allocations | 1,700,000 | 1,050,000 | 1,100,000 |
If an incentive bonus is paid to the manager who achieved the highest operating income before support department allocations, it follows that
a.Division B's manager is given the bonus
b.Divisions B and C's managers divide the bonus
c.Division A's manager is given the bonus
d.Division C's manager is given the bonus
44.
Operating income for Division L is $250,000, total support department allocations are $400,000, and operating expenses are $2,750,000. The revenues for Division L are
a.$3,000,000
b.$3,400,000
c.$2,750,000
d.$650,000
In: Accounting
Please explain these:
34. Which solution has the highest pH?
Ka:
HCN 5.8×10–10
CH3COOH 1.8×10–5
(A) 0.10 M CH3COOH (B) 0.10 M HCN (C) 0.10 M CH3COOK (D) 0.10 M NaBr
7. A dilute solution of which acid is most likely to produce a reduction product other than H2 when it reacts with a metal? (A) HF (B) HCl (C) HNO3 (D) H2SO4
35. A 75 mL solution that is 0.10 M in HC2H3O2 and 0.10 M in NaC2H3O2 has a pH of 4.74. Which of the following actions will change the pH of this solution?
I Adding 15 mL of 0.10 M HCl
II Adding 0.010 mol of NaC2H3O2
III Diluting the solution from 75 mL to 125 mL
(A) I only (B) II only (C) I and II only (D) I, II and III
Solutions:
34) C
7) C
35) C
In: Chemistry
18.Rank the following bonds, from highest to lowest interest rate risk: 2-year zero coupon, 2-year 5% coupon bond, 30-year 5% coupon bond, 30-year, zero coupon bond.
A.30-year zero coupon bond, 30-year 5% coupon bond, 2-year 5% coupon bond, 2-year zero coupon bond
B.30-year zero coupon bond, 30-year 5% coupon bond, 2-year zero coupon bond, 2-year 5% coupon bond
C.30-year 5% coupon bond, 30-year zero coupon bond, 2-year 5% coupon bond, 2-year zero coupon bond
D.2-year 5% coupon bond, 2-year zero coupon bond, 30-year 5% coupon bond, 30-year zero coupon bond
E.2-year zero coupon bond, 2-year 5% coupon bond, 30-year 5% coupon bond, 30-year zero coupon bond
19.A corporate bond with a 5.75 percent coupon has 15 years left to maturity. It has had a credit rating of BB and a yield to maturity of 6.25 percent. The firm has recently gotten more financially stable and the rating agency is upgrading the bonds to BBB. Thenew appropriate discount rate will be 6.00 percent. What will be the change in the bond's price in dollars? (Assume interest payments are paid semi-annually and a par value of $1,000.)
A.increase $28.75
B.decrease $22.25
C.increase $22.25
D.decrease $23.72
E.increase $23.72
20.A 6.00percent coupon bond with 12 years left to maturity is priced to offer a 6.50percent yield to maturity. You believe that in one year, the yield to maturity will be 6.25 percent. What is the change in price the bondwill experience in dollars? (Assume semi-annual interest payments and $1,000 par value.)A.$12.50B.$19.67C.$20.22D.$21.55E.$25.00
In: Finance