Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

1. An experiment consists of drawing two marbles from a box containing red, yellow, and green marbles. One event in the sample space is RR. What are all of the events in the sample space? (Note: order matters) (3)

2. In a certain large population, 46% of households have a total annual income of over $70,000. A simple random sample is taken of four of these households. What is the probability that more than 2 of the households in the survey have an annual income of over $70,000?                                                                (8)

3. Which would you expect to have a higher standard deviation: data scores that are spread out or data scores that are close together?   
4. In a survey of U.S. households, 588 had home computers while 722 did not. Use this sample to estimate the probability of a household having a home computer.

1. Home Security Systems is studying the time utilization of its sales force. A random sample of 40 sales calls showed that the representatives spend an average of ẍ = 44 minutes on the road with a standard deviation of s = 6 minutes for each sales call.

1. Create a line showing the mean and values for 4 standard deviations above and 4 standard deviations below the mean.                                                                                                                                                (2)

2. Use Chebyshev’s Theorem to find the values between which we can expect at least 89% of the data to fall.                                                                                                                                                                       (2)

3. At least what percent of the data can we expect to fall between 38 and 50 minutes using the Empirical Rule?                                                                                                                                                        (2)

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had a distribution where the possible values of X are 1, 2, 3, 4 with the corresponding probabilities of 0.2, 0.4, 0.3, and 0.1. Use this information to answer questions 20-23 below.

2. Does the above data form a probability distribution? Create the distribution and explain why or why not.(5)

3. Using the above data, what is the probability that a randomly chosen subject completes at least three puzzles in the five-minute period while listening to soothing music?                                                                   (2)

4. Using the above data, the mean µ of X is what? Show work.                                                                             (3)
5. Using the above data (on previous page), the standard deviation σ of X is what? Show work.                      (4)

1. Why would we use the 10-90 percentile range?                                                                                                  +2

2. A data set has a range of 348. Use the range rule of thumb to determine the standard deviation.        +1

A batch of 26 light bulbs includes 5 that are defective. Two light bulbs are randomly selected. If the random variable, X, represents the number of defective light bulbs which can be selected, what values can X have?                

An important quality characteristic used by the manufacturers of ABC asphalt shingles is the amount of moisture the shingles contain when they are packaged. Customers may feel that they have purchased a product lacking in quality if they find moisture and wet shingles inside the packaging. In some cases, excessive moisture can cause the granules attached to the shingles for texture and colouring purposes to fall off the shingles resulting in appearance problems. To monitor the amount of moisture present, the company conducts moisture tests. A shingle is weighed and then dried. The shingle is then reweighed, and based on the amount of moisture taken out of the product, the pounds of moisture per 100 square feet is calculated. The company would like to show that the mean moisture content is less than 0.35 pound per 100 square feet. The file (A & B shingles.csv) includes 36 measurements (in pounds per 100 square feet) for A shingles and 31 for B shingles. 3.1. For the A shingles, form the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet. 3.2. For the A shingles, conduct the test of hypothesis and find the p-value. Interpret the p-value. Is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet? 3.3. For the B shingles, form the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet. 3.4. For the B shingles, conduct the test of the hypothesis and find the p-value. Interpret the p-value. Is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet? 3.5. Do you think that the population means for shingles A and B are equal? Form the hypothesis and conduct the test of the hypothesis. What assumption do you need to check before the test for equality of means is performed? 3.6. What assumption about the population distribution is needed in order to conduct the hypothesis tests above? 3.7. Check the assumptions made with histograms, boxplots, normal probability plots or empirical rule. 3.8. Do you think that the assumption needed in order to conduct the hypothesis tests above is valid? Explain.and please send me python commands

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory. In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

Month 1 2 3 4

Quality control measures: Number of defects 190 168 129 90

Number of warranty claims 51 44 35 32

Number of customer complaints 107 101 84 63

Material control measures: Purchase order lead time 8 days 7 days 5 days 4 days Scrap as a percent of total cost 1% 1% 2% 3%

Machine performance measures: Machine downtime as a percentage of availability 3% 4% 4% 6%

Use as a percentage of availability 94% 91% 88% 84%

Setup time (hours) 8 10 11 12

Delivery performance measures: Throughput time ? ? ? ? Manufacturing cycle efficiency (MCE) ? ? ? ? Delivery cycle time ? ? ? ?

Percentage of on-time deliveries 95 % 94 % 91 % 88 %

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Average per Month (in days) 1 2 3 4

Wait time per order before start of production 9.0 11.4 12.0 14.0

Inspection time per unit 0.9 0.7 0.7 0.7

Process time per unit 2.8 2.0 1.6 1.2

Queue time per unit 3.0 4.3 5.1 7.4

Move time per unit 0.3 0.6 0.6 0.7

Required: 1-a. Compute the throughput time for each month. 1-b. Compute the manufacturing cycle efficiency (MCE) for each month. 1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the manufacturing cycle efficiency (MCE) for each month.

1-c. Compute the delivery cycle time for each month.

3-a. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 5 the inspection time, process time, and so forth, are the same as for month 4, except that the company is able to completely eliminate the queue time during production using Lean Production. Compute the new throughput time and MCE.

3-b. Refer to the inspection time, process time, and so forth, given for month 4. Assume that in month 6 the inspection time, process time, and so forth, are the same as in month 4, except that the company is able to eliminate both the queue time during production and the inspection time using Lean Production. Compute the new throughput time and MCE.

Tombro Industries is in the process of automating one of its plants and developing a flexible manufacturing system. The company is finding it necessary to make many changes in operating procedures. Progress has been slow, particularly in trying to develop new performance measures for the factory.

In an effort to evaluate performance and determine where improvements can be made, management has gathered the following data relating to activities over the last four months:

The president has read in industry journals that throughput time, MCE, and delivery cycle time are important measures of performance, but no one is sure how they are computed. You have been asked to assist the company, and you have gathered the following data relating to these measures:

For each question on a multiple-choice test, there are five possible answers of which exactly one is correct for each question. Assume there are 10 questions on the test and a student selects one answer for each question at random. Let X be the number of correct answers he or she gets.

a) How is X distributed? (Specify the values of the corresponding parameters).

b) Find P(X < 6) and P(X = 6). c) Find E(X) and V ar(X).

2. Suppose that a basketball player makes a free throw 60% of the time. Let X equal the number of free throws that this player must attempt to make a total of 3 shots. Assume independence among attempts,

a) How is X distributed? (Specify the values of the corresponding parameters)

b) Find P(X = 6).

c) Find E(X) and V ar(X). 2 3.

A factory puts biscuits into boxes of 100. The probability that a biscuit is broken is 0.03. Find the probability that a box contains 2 broken biscuits using Poisson approximation.

4. (20 pts) Let X have the p.d.f: f(x) = 3x 2 2 for −1 ≤ x ≤ 1 and f(x) = 0 for otherwise . a) Find P(X > 0.5). b) Find E(X). 3 c) Find the c.d.f F(x). d) Find π0.5. 4

5. (10 pts) Suppose that a system contains a certain type of component whose time, in years, to failure is given by X. The random variable X is modeled nicely by the exponential distribution with mean time to failure θ = 3. Find: a) P(X ≥ 4). b) Given that the component has been in operation for 2 years, find the conditional probability that it will last for at least another 4 years. 5

6. (8 pts) If X ∼ N(−10, 25), find: a) P(X ≤ 0) b) P(−15 ≤ X ≤ −5) c) P(X ≤ 20) d) π0.4.

7. (6 pts) If Z ∼ N(0, 1), find the values of z such that: a) P(Z > z) = 0.3. b) P(|Z| ≤ z) = 0.4. 6

8. (21 pts) Jim sells blueberry bushes to his customers when they are at least 18 inches tall. He wants to know how long it will take each of his blueberry bushes to grow tall enough to sell. To get an estimate of this time, he selects ten plants at random and records the number of days each one takes to grow from a seed into an 18 inch tall plant. 96, 98, 97, 101, 98, 95, 100, 95, 98, 101. Find the values of the following statistics a) Sample mean ¯x b) Sample median ˜x. c) Sample mode and sample range. d) Sample variance and sample standard deviation.

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, , for Stock B ( = 10.60%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 25.58%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

   Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

   Is it possible that most investors might regard Stock B as being less risky than Stock A?

   1. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   4. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   
   
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3. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.

   Stock A:

   Stock B:

   Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?

   1. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   3. In a stand-alone risk sense A is less risky than B. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   4. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   5. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.