Questions
1) The first task is to review some information that might be useful later: a) Write...

1) The first task is to review some information that might be useful later:

a) Write a brief definition of the word "quartile" as we have used it in previous weeks. Be sure to provide a citation: _____________________________.

b) Write a brief definition of the word "quantile" as it might be used in statistics. Be sure to provide a citation (do not cut and paste... use your own words to summarize what you discovered): ________________________________.

c) From within interactive R, enter the command shown below (the command shows a help page for the pbinom command). Provide a very brief description of the arguments that are passed to the pbinom() command ("arguments" in computer programming are the options that you give to a function so that the function can calculate what you want it to). Note that one of the arguments is lower.tail = TRUE, and because there is a value assigned to it with the equals sign, it means that if you do not enter a new value for lower.tail, it will be set to TRUE by default. Do not type the ">" into R, it is the command prompt:

> ?pbinom

2) You can use the dbinom() command (function) in R to determine the probability of getting 0 heads when you flip a fair coin four times (the probability of getting heads is 0.5):

dbinom(0, size=4, prob=0.5)

Find the equivalent values for getting 1, 2, 3, or 4 heads when you flip the coin four times. TIP: after you run the first dbinom() command, press the up arrow and make a small change and run it again.

probability of getting exactly 1 head: _______

probability of getting exactly 2 heads: _______

probability of getting exactly 3 heads: _______

probability of getting exactly 4 heads: _______

3) Use the pbinom() function in R to show the cumulative probability of getting 0, 1, 2, 3, or 4 heads when you flip the coin 4 times (this is the same as finding the probability than the value is less than or equal to 0, 1, 2, 3, or 4.)

probability of getting no more than 0 heads: ____

probability of getting no more than 1 head: _____

probability of getting no more than 2 heads:_____

probability of getting no more than 3 heads: ____

probability of getting no more than 4 heads: ____

4) The following R command will show the probability of exactly 6 successes in an experiment that has 10 trials in which the probability of success for each trial is 0.5:

dbinom(6, size=10, prob=0.5)
(True/False)____________

5) What is the probability of getting fewer than 2 heads when you flip a fair coin 3 times (round to 2 decimal places) ? ______

6) What is the probability of getting no more than 3 heads when you flip a fair coin 5 times (be sure to understand the wording differences between this question and the previous one—round to 2 decimal places)? ________

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Information

The exponential distribution is a continuous distribution. The main R functions that we will use for the exponential distribution are pexp() and qexp(). Here is an example of the pexp() function. Leaves are falling from a tree at a rate of 10 leaves per minute. The rate is 10, or we can say that lambda = 10 (meaning 10 leaves fall per minute). The leaves do not fall like clockwork, so the time between leaves falling varies. If the time between leaves falling can be modeled with an exponential distribution, then the probability that the time between leaves falling will be less than 5 seconds (which is 5/60 of a minute) would be:

(note: this is an explanation of how pexp() works, you will answer a different question below)

pexp(5/60, rate=10)

which is about 0.565 (meaning that the probability is a bit higher than 50% that the next time-span between leaves falling will be less than 5 seconds).

For tasks 7-12, assume that the time interval between customers entering your store can be modeled using an exponential distribution. You know that you have an average of 4 customers per minute, so the rate is 4, or you can say that lambda =4.

It is easiest to keep everything in the original units of measurement (minutes), but you can also translate that to seconds because a rate of “4 customers per minute” is the same as “4 customer per 60 seconds,” and you can divide each number by 4 to get a rate of “1 customer per 15 seconds” or a rate of “1/15 customers per second.”

7) What is the expectation for the time interval between customers entering the store? Be sure to specify the units of measurement in your answer. Round to 3 decimal places: ___________________

8) What is the variance of the the time interval? Be sure to specify the units of measurement in your answer. Round to 3 decimal places:_________________

9) The pexp() function is introduced at the bottom of Yakir, 2011, p. 79, and there are some tips above. What is the probability that the time interval between customers entering the store will be less than 15.5 seconds. Be sure to enter values so that everything is in the same unit of measurement. Be sure to specify the units of measurement in your answer. Round your answer to 3 decimal places: _________________.

10) What is the probability that the time interval between customers entering the store will be between 10.7 seconds and 40.2 seconds?________

11) The qexp() function in R allows you to enter a probability, and it will tell you the criterion value (“cutoff point”) that corresponds to that probability value (e.g., if you enter .05 it tells you the cutoff point below which 5% of the values in the distribution fall).

What value of x would be the criterion value (cut-off point) for the top 5% of time intervals (Round to 3 decimal places, and include the units of measurement)? _______

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12) Describe in your own words the meaning of the number that the following R command produces (you are asked to interpret the resulting number so that we understand what that number means).

pexp(1.2, rate=3)

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Information

You have now had practice with the binomial distribution and the exponential distribution. The approach to solving problems for the normal distribution is similar to that for the exponential function, but obviously you use different R functions (usually pnorm() or qnorm()).

For the following three exercises, assume that you have a normally distributed random variable, called A, with a mean of 7, and a population standard deviation of 3.

13) What is the probability that a randomly selected value from variable A will be greater than 9?_______

14) What value of variable A would be the cutoff point (criterion value) for identifying the lowest 4% of values in variable A (use the qnorm function)?____________

15) What is the probability that a randomly selected value from variable A will be more than one standard deviation above its mean (there are couple ways to solve this, one way is to use the standard normal distribution?________________

In: Math

Problem 8-18B Comprehensive Variance Analysis [LO8-4, LO8-5, LO8-6] Michiana Company's Benton Harbor Plant produces precast ingots...

Problem 8-18B Comprehensive Variance Analysis [LO8-4, LO8-5, LO8-6] Michiana Company's Benton Harbor Plant produces precast ingots for industrial use. Angelo Lorenzo, who was recently appointed general manager of the Benton Harbor Plant, has just been handed the plant’s contribution format income statement for October. The statement is shown below: Budgeted Actual Sales (5,000 ingots) $ 235,000 $ 235,000 Variable expenses: Variable cost of goods sold* 71,350 86,370 Variable selling expenses 13,000 13,000 Total variable expenses 84,350 99,370 Contribution margin 150,650 135,630 Fixed expenses: Manufacturing overhead 62,000 62,000 Selling and administrative 77,000 77,000 Total fixed expenses 139,000 139,000 Net operating income (loss) $ 11,650 $ (3,370) *Contains direct materials, direct labor, and variable manufacturing overhead. Mr. Lorenzo was shocked to see the loss for the month, particularly because sales were exactly as budgeted. He stated, "I sure hope the plant has a standard cost system in operation. If it doesn't, I won't have the slightest idea of where to start looking for the problem." The plant does use a standard cost system, with the following standard variable cost per ingot: Standard Quantity or Hours Standard Price or Rate Standard Cost Direct materials 3.8 pounds $ 2.20 per pound $ 8.36 Direct labor 0.7 hours $ 6.80 per hour 4.76 Variable manufacturing overhead 0.5 hours* $ 2.30 per hour 1.15 Total standard variable cost $ 14.27 *Based on machine-hours. During October the plant produced 5,000 ingots and incurred the following costs: a. Purchased 24,000 pounds of materials at a cost of $2.65 per pound. There were no raw materials in inventory at the beginning of the month. b. Used 18,800 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.) c. Worked 4,100 direct labor-hours at a cost of $6.50 per hour. d. Incurred a total variable manufacturing overhead cost of $7,560 for the month. A total of 2,800 machine-hours was recorded. It is the company’s policy to close all variances to cost of goods sold on a monthly basis. Required: 1. Assume that the company recognizes price variances when materials are purchased. Compute the following variances for October: a. Direct materials price and quantity variances. (Input all amounts as positive values. Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance).) b. Direct labor rate and efficiency variances. (Input all amounts as positive values. Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance).) c. Variable overhead rate and efficiency variances. (Input all amounts as positive values. Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance).) 2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for October. (Input all amounts as positive values. Indicate the effect of variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance).) 3. Pick out the two most significant variances that you computed in (1) above. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.) Materials price variance Materials quantity variance Variable overhead efficiency variance Labor rate variance Variable overhead rate variance Labor efficiency variance

In: Accounting

Reliable company specializes in homemade biscuits and receives all income from sales. The sales estimates (in...

Reliable company specializes in homemade biscuits and receives all income from sales. The sales estimates (in million$) for the four quarters for the company are as follows: 01 = 600, Q2 = 500, Q3 = 550, Q4 = 640. The average collection period for accounts receivables is 45 days. Beginning receivables (Q1 beginning) is $300 million. The purchases are 50, of next quarter sales. Beginning payables (Q1 beginning) is $100 million. The accounts payable period is 45 days. The beginning cash balance (Q1 beginning) is $50 million so how much will be the cash balance at the end of Quarter 2

In: Accounting

Reliable company specializes in homemade biscuits and receives all income from sales. The sales estimates (in...

Reliable company specializes in homemade biscuits and receives all income from sales. The sales estimates (in million$) for the four quarters for the company are as follows: 01 = 600, Q2 = 500, Q3 = 550, Q4 = 640. The average collection period for accounts receivables is 45 days. Beginning receivables (Q1 beginning) is $300 million. The purchases are 50, of next quarter sales. Beginning payables (Q1 beginning) is $100 million. The accounts payable period is 45 days. The beginning cash balance (Q1 beginning) is $50 million so how much will be the cash balance at the end of Quarter 2

In: Accounting

Published data show that during the previous quarter (3 months) employment has risen that demand-pull inflation...

  1. Published data show that during the previous quarter (3 months) employment has risen that demand-pull inflation is rising. These indicators suggest that the growth of GDP is likely to increase in this or the next quarter.

Indicate     T   F    #

Explanation: [Limit 40 words: 2 marks]

  1. A good leading indicator of changes in the rate of inflation during economic cycles is the change in the growth rate of the money supply.

Indicate     T   F    #

Explanation: [Limit 40 words: 2 marks]

  1. In Australia the index of consumer sentiment is usually a leading indicator.

Indicate     T   F    #

Explanation: [Limit 40 words: 2 marks]

In: Economics

Consider the quarterly demand of 3500, 2600, 5500, 4400, for quarters 1,2,3,4, respectively. Let the production...

Consider the quarterly demand of 3500, 2600, 5500, 4400, for quarters 1,2,3,4, respectively. Let the production standard be 250 items/quarter. Let the carrying cost be $5/item/quarter.

If the beginning annual inventory is 500 but the ending annual inventory objective is 620,

then what is the total annual carrying cost for the aggregate planning strategies listed?

Select One

Answer

Aggregate Planning

Strategy

Total Annual

Carrying Cost

A

Level Capacity

25500

B

Chase Demand

11200

C

Level Capacity

6375

D

Chase Demand

11500

E

None of the above

In: Accounting

A young engineer decides to save $240 per year toward retirement in 40 years. If he...

A young engineer decides to save $240 per year toward retirement in 40 years.

  1. If he invests this sum at the end of every year at 9%, then how much will be accumulated by retirement time?
  2. If by astute investing the interest rate could be raised to 12%, then what sum could be saved?
  3. If he deposits one fourth of this annual amount each quarter ($60 per quarter) in an interest bearing account earning a nominal annual interest rate of 12%, compounded quarterly, how much could be saved by retirement time?
  4. In part (c), then what annual effective interest rate is being earned?

In: Finance

Do in excel please. Sales Budget (Learning Objective 2) Jefferson Sports Medicine, Inc., offers two types...

Do in excel please.

Sales Budget (Learning Objective 2)

Jefferson Sports Medicine, Inc., offers two types of physical exams for students: the basic physical and the extended physical. The charge for the basic physical is $60, while the charge for the extended physical is $135. Jefferson expects to perform 220 basic physicals and 190 extended physicals in July, 235 basic and 200 extended in August, and 105 basic and 110 extended in September. Prepare the sales budget for the service revenue expected from the physical exams performed for the second quarter (July through September), with a column for each month and for the quarter in total.

In: Accounting

At an emergency room at one hospital, the nurses are convinced that the number of patients...

At an emergency room at one hospital, the nurses are convinced that the number of patients that they see during the midnight shift is affected by the phases of the moon. The doctors think this is an old wives’ tale. The nurses decide to test their theory at the 0.10 level of significance by recording the number of patients they see during the midnight shift for each moon phase over the course of one lunar cycle. The results are summarized in the table below. Perform a test for goodness of fit.

ER Patients During the Midnight Shifts :Number of Patients: New Moon 85 ,1st Quarter 66 ,Full Moon 97, 3rd Quarter 68

In: Statistics and Probability

Investment analysts at a leading investment bank reported in October 2002 that the revenues of Reuters...

Investment analysts at a leading investment bank reported in October 2002 that the revenues of Reuters had slumped in the third quarter of its financial year, that recovery was still some way off and that the company would be reporting poor third quarter results in the following week. The company had already launched a restructuring plan, involving a large cut in the workforce to restore profit margins on sales of its information terminals.

(Reported New York Times, November 2002)

Required:

Discuss and explain how do you think the analysts' report might affect the relationship between the company and its investors?


In: Accounting