QUESTION 1

1. Which of the following statements is TRUE?

   	a.	The average amount of safety stock depends on the size of orders placed with the supplier.
   	b.	The average amount of safety stock depends on the frequency in which orders are placed with the supplier.
   	c.	Cycle stock is the amount of inventory on hand when an order from the supplier is placed.
   	d.	Safety stock is the expected amount of inventory on hand when an order arrives from the supplier.
   	e.	All four answer choices are TRUE

1 points   

QUESTION 2

1. Consider an oilfield service company ( OSC ) that stocks a specific type of compressor, which they source from an American supplier. Since this compressor is the only product that OSC sources from that specific supplier, and given relatively steady demand of 2,000 compressors throughout the year, OSC uses a Continuous Review (Q) system for managing the inventory of this compressor. Orders to replenish stock requires administrative and other work that is estimated to be $40 per order. The compressors are purchased from the supplier for $325 each. It is estimated that annual inventory holding costs are 27% of the value of the item. The time from when an order is placed with the supplier until it arrives averages three weeks (including time to clear customs).

   What is the order quantity that OSC should use for these compressors if they wish to minimize total annual holding and ordering costs?

   	a.	115
   	b.	44
   	c.	22
   	d.	52
   	e.	43

1 points   

QUESTION 3

1. The Cheezy-Pretz corporation manufactures and distributes cheese-coated pretzels. They purchase their cheese, which come from a specific supplier in 10 kg packages, in batches of 500 kg (i.e. they currently order in lots of 50 packages at a time). This amounts to approximately an order every month, since annual demand is 600 packages. Each package costs Cheezy-Pretz $7, and they estimate that holding a package in inventory costs $1.75 per year. Further, they have studied their ordering process and estimate that it costs them $35 to place an order. They have been told that if they find the optimal order quantity, they could save money on annual ordering plus holding costs. Cheezy-Pretz would like to know how much they would save per year in ordering plus holding costs if they used the EOQ rather than their current order quantity of 50 packages at a time.

   	a.	<$100 per year
   	b.	>100 per year but < $150 per year
   	c.	>$150 per year but < $200 per year
   	d.	>$200 per year but < $250 per year
   	e.	>$300 per year

QUESTION 4

1. A night club that operates seven days a week uses a periodic review system where they check the stock of beer and liquor every Tuesday (at noon) and place an order that arrives on Thursday (at noon). They have found that demand for Silk beer ( smooth as silk ) averages 4.5 units per day with a standard deviation of 1.75 units. In any given week, they would like to be 95% sure that they don’ t run out of Silk beer before their order arrives. On Tuesday, if they have 16 units of beer on hand, how many units should they order?

   	a.	38
   	b.	39
   	c.	34
   	d.	23
   	e.	43

1 points   

QUESTION 5

1. The QRS Restaurant Supplier Co. is a wholesaler/distributor that supplies clients in the restaurant business with fresh perishables (e.g., produce) as well as equipment and supplies. One product that QRS provides to their customers (restaurants) is plastic stretch-wrap that comes in special extra-large rolls. QRS sells rolls from their inventory to their customers, and the inventory at the QRS warehouse is replenished by the stretch-wrap manufacturer in Ann Arbor, MI.

   QRS collected the following specific inventory-related data :
   
   Weekly demand (in rolls): average 42/week; standard deviation 16/week
   
   Annual demand (in rolls; assuming that demand occurs 52 weeks/year): 2,184
   
   Purchase price (QRS pays manufacturer) per roll: $54 Canadian
   
   QRS cost to place order with manufacturer: $35 per order (includes administrative costs to issue purchase order, invoice payment, etc.)
   
   XYZ annual cost to hold inventory: 23% of value
   
   Lead time for replenishment from manufacturer: three weeks
   
   Your Question: QRS currently places a replenishment order for rolls when their inventory position reaches 160 units. What cycle-service level does this imply?

   	a.	98.9%
   	b.	73.9%
   	c.	89.0%
   	d.	96.4%
   	e.	92.9%

QUESTION 6

1. Which of the following statements is TRUE?:

   	a.	A Periodic Review system requires less safety stock than a Continuous Review system.
   	b.	Over the long run, a Periodic Review (P) system and a Continuous Review (Q) system will generally have the same average order frequency and order size as each other (assuming that the manager aims to minimize the total of annual holding and ordering costs in both of the cases).
   	c.	In a Periodic Review system, order quantities tend to remain the same from order to order, while in a Continuous Review system, order quantities tend to vary from order to order.
   	d.	A Periodic Review system requires a computerized record-keeping system to maintain constant awareness of inventory position.
   	e.	All four answer choices are TRUE

QUESTION 7

1. A gas processing plant has a vat of important industrial lubricant for the machinery at the plant. Since an external supplier is responsible for maintaining the inventory of the lubricant, the supplier has a sensor set up on the vat that sends them a notification (by text message) as soon as the vat reaches a specific level of remaining volume. The demand for the lubricant averages 19 litres per day (with a standard deviation of 4.5), and the supplier requires a four-day lead time to refill the vat (assume it is exactly four days with no variability). If the supplier wishes to promise a 97.5% cycle-service level, at what volume should the sensor be set to contact the supplier? (Please double-check your answer, even if it shows up as one of the choices below.)

   	a.	76
   	b.	112
   	c.	94
   	d.	85

Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with μ = 50 and σ = 7.5, with high scores indicating high satisfaction. An SRS of n= 36 is taken from this population. What is the standard error (SE) of x for these data? We seek to discover if a particular group of patients comes from this population in which μ = 50. Sketch the curve that describes the sampling distribution of the sample mean under the null hypothesis. Mark the horizontal axis with values that are ±1, ±2, and ±3 standard errors above and below the mean. Suppose in a sample of n= 36 from this particular group of patients the mean value of x is 48.8. Mark this finding on the horizontal axis of your sketch. Then compute a z statistic for this scenario and make sure it matches your sketch. What is the two-sided alternative hypothesis for this scenario? Find the corresponding p-value for your z-statistic using Table B. Draw a conclusion for this study scenario based on your results

The number of products sold for the past several months is given along with the forecasts using both 3-month moving average and exponential smoothing (α = .2). Determine the better forecast using the MSE.

The Easy Credit Company report the following table representing a breakdown of customers accounting to the amount they owe and whether a cash advance has been made. An auditor randomly selects one of the accounts.

Show your work!

1. What is the probability that a customer received a cash advance?
2. What is the probability that a customer owed less than $200 and received a cash advance?
3. What is the probability that a customer owed less than $200 or received a cash advance?
4. Given that the customer-owned $1000 or more, what is the probability that the customer received a cash advance?
5. Are the events "receiving a cash advance" and "owning $1000 or more" independent? Explain why or why not.

You would like to make a nutritious meal of eggs, edamame and elbow macaroni. The meal should provide at least 30g of carbohydrates, at least 20g of protein, and no more than 60g of fat. An egg contains 2g of carbohydrates, 17g of protein, and 14g of fat. A serving of edamame contains 12g of carbohydrates, 12g of protein and 6 g of fat. A serving of elbow macaroni contains 43g of carbohydrates, 8g of protein, and 1g of fat. An egg costs $2, a serving of edamame costs $5, and a serving of elbow macaroni costs $3. Formulate a linear optimization model that could be used to determine the number of servings of egg, edamame, and elbow macaroni that should be in the meal in order to meet the nutrition requirements at minimal cost.

Question 10:

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 494 and a standard deviation of 39.

According to the standard deviation rule, approximately 68% of the students spent between $_____ and $ ______ on textbooks in a semester.

Question 11:

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 16.

According to the standard deviation rule, _____ % of people have an IQ between 52 and 148. Do not round.

Question 12:

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 19.

According to the standard deviation rule, only ______ % of people have an IQ over 157.

Question 13:

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 429 and a standard deviation of: σ= 23.

According to the standard deviation rule, almost 16% of the students spent more than what amount of money on textbooks in a semester?

Running times (Y) and maximal aerobic capacity (X) for 14 female
Runners. Data collected for running times and maximal aerobic capacity are listed
below
X: 61.32 55.29 52.83 57.94 53.31 51.32 52.18 52.37 57.91 53.93 47.88 47.41
47.17 51.05
Y: 39.37 39.80 40.03 41.32 42.03 42.37 43.93 44.90 44.90 45.12 45.60 46.03
47.83 48.55
(a) Calculate the mean, median, MAD, MSD, and standard deviation for each
variable. ? [Include all your steps and explain all the steps involved in details]
(b) Which of these statistics give a measure of the center of data and which give a
measure of the spread of data? [Explain in your own words]
(c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y
against X. [Use excel for scatterplot, show all your computations concerning
the correlation and explain all your steps]
(d) Why is it inappropriate to calculate the autocorrelation of these data? [Explain in
your own words]

PLEASE SHOW ANSWER WORKED CALCULATIONS ON EXCEL AS PER QUESTION REQUIREMENTS.

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

5.54 A survey by Frank N.Magid Associates revealed that 3% of Americans are not connected to the Internet at home. Another researcher randomly selects 70 Americans. a. What is the expected number of these who would not be connected to the Internet at home?
b. What is the probability that eight or more are not connected to the Internet at home? c. What is the probability that between three and six (inclusive) are not connected to the Internet at home?

5.51 An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River.Suppose six of the office workers are randomly selected. a. What is the probability that all six workers commute from the west side of the Rio Grande?

b. What is the probability that none of the workers commute from the west side of the Rio Grande?

c. Which probability from parts (a) and (b) was greatest? Why do you think this is?

d. What is the probability that half of the workers do not commute from the west side of the Rio Grande?

Alice and Bob are supposed to meet in the cafeteria. Alice arrives at a random time between
noon and 1pm, and wait for 15 minutes upon her arrival and then leaves. Bob also also arrives
at a random time between noon and 1 pm, but waits up to 20 minutes and then leaves.
(a) What is the probability that Bob arrives before 12:20?
(b) What is the probability that Alice and Bob meet?
(c) If Bob arrives later than Alice, what is the probability that they meet?
(d) Suppose that Alice and Bob have managed to meet. What is the probability that Bob
has arrived before 12:20?

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6,P(B) = 0.4,and P(A ∩ B) = 0.3,suppose that P(C) = 0.2,P(A ∩ C) = 0.12,P(B ∩ C) = 0.1, and P(A ∩ B ∩ C) = 0.08.

a)What is the probability that the selected student has at least one of the three types of cards?

b)What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card?

c)Calculate P(B | A)and P(A | B).

P(B | A)=

P(A | B)=

d)If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard?

e)Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?

A bias coin has the probability 2/3 of turning up heads. The coin is thrown 4 times.
(a) What is the probability that the total number of heads shown is 3?
(b) Suppose that we know that outcome of the first throw is a head. Find the probability
that the total number of heads shown is 3.
(c) If we know that the total number of heads shown is 3, find the probability that the outcome
of the first throw was heads.

At a Midwestern business school, historical data indicates that 70% of admitted MBA students ultimately join the business school’s MBA program. In a certain year, the MBA program at the University admitted 200 students.

a. Find the probability that at least 150 students ultimately join the MBA program.

b. Find the probability that no less than 135 and no more than 160 students finally join the MBA program.

c. How many students should the MBA program expect to join the program?

d. What is the standard deviation of the number of students who will join the MBA program? e. Let X be the number of students out of 200 who will join the program. Would the empirical rule apply to the probability distribution of X in this case?