Suppose the amount of time to finish assembling a component is exponentially distributed with an average of 2 minutes.

(a) What is the probability that it takes more than 5 minutes to assemble a component? (b) If 100 components are randomly selected, what is the probability that the average amount of time to assemble these100 components is more than 2.3 minutes?

Make Versus Buy Case ABC Ltd. is a manufacturing company engaged in the manufacturing of valves. They have been in the business for last 3 years and have been manufacturing only one type of valves. They started their business initially with sales of 10,000 valves per month and now they have grown the volume to about 50,000 valves per month. They have been buying all the raw material for the valve and were doing all the manufacturing in house. Now they have established themselves in the market and are planning to expand and produce different varieties of valves. They have their plant in the main city and the total area of the plant is 50,000 sq. ft. Now if they want to expand and continue doing all the activities of manufacturing of all the varieties in house, they would need another 50,000 Square feet of the area. In the recent times, the land prices in the area have more than doubled in the last 3 years and still land is available with great difficulty. Mr Mohan is the production head of ABC Ltd. and has been successful with the production and the level is continuously increasing. But in recent times, he is facing the problem of quality complaints which have gone up from average 0.2 % in previous 2 years to 0.5 % this year. Also, he is finding that there is a high level of dissatisfaction among the workers regarding workload as well as salary levels. The workers are regularly complaining about the over work. Although, Mr Mohan has found that the workers have been spending lot of time on tea breaks, lunch breaks and even in between the production spending lot of time talking to each other. But, due to insufficient workers and staff, he is unable to take strict action and the workers are taking advantage of this situation. For completing the work and delivering the products timely, he has to employ workers on overtime and his overtime cost has also increased 3 times. Mr Mohan is worried about the new expansion plan of the management and is worried where the new workers would come from as he is already finding shortage of workers for the existing job. He has requested the management not to go for expansion immediately and look at improving and consolidating the existing set up. He has sent his request to Mr S. Kumar Director – Operations. Mr Kumar has gone through the request of Mr Mohan and called a meeting of all the department heads and explained the situation to all concerned. The marketing manager has expressed very bullish prospect about the company’s growth and said that the company should take advantage of growing economy and established brand image of the company and definitely go for expansion. The finance manager also expressed that this will result in economy of scale for the products and will further increase the profitability of the products. Mr Mohan again expressed his problems regarding availability of manpower as well as production control and effect on quality and productivity. The Marketing manager asked the Production manager about the option of outsourcing. Mr Mohan is sceptical about the outsourcing option as he felt that the outside agency will always charge more as he will try to make his profit as well and also is worried about the possible problems of deliveries. Mr Kumar asked the Mr Naresh who is the Purchase manager about his views. He said that since the suppliers would also be interested in doing the business, they would not like to delay as with delay they also incur loss. The Finance manager said that we can look at cost comparison for buying against in house manufacturing. After listening to all the views, Mr Kumar told Mr Mohan to work out the cost of production for future sales as per the forecast given by the Marketing department. He also told Mr Naresh to collect the details of the future requirements to get the purchase cost details for few components of the valve. Mr Mohan and Mr Naresh have collected their data and they have presented the data in the meeting called by Mr Kumar to review the plan. First the marketing head Mr Suresh presented his market forecast and then Mr Mohan presented his report and explained the details as follows. One supervisor with monthly salary of $5000 with expected increase of 10 % per year. Direct wages of worker as $4 per unit. With 10 % reduction in second year, no change in 3rd year and increase of 10 % every subsequent year. Material cost of $14 per unit with an increase of 10 % every year. Power and fuel cost of $2 per unit with increase of 10 % every year. Indirect labour as 50 % of direct labour. They will have to buy a new machine with a cost of $50 lac. With usable life of 5 years Mr Naresh explained his details as follows: Component price from supplier at $20 for the first 2 years with an increase of 10 % every subsequent year. Transportation cost of $2 per unit for the first year with increase of $0.20 every subsequent year. Inventory cost (storage cost) as 5 % per year of the basic material cost. The Marketing manager has given the sales forecast for next 5 years as follows:

Year                1                     2                      3                      4                      5

Sales quantity 300000             500000            700000            900000            1000000

Questions 1. Based on this data, is it economical for ABC Ltd.to go for buying the product from market or manufacturing in house.

Question 2. What other factors should ABC Ltd. look at for making this decision?

Question 3. What factors of quality are important to make the final decision whether to manufacture in house or procure?

Reasonable assumptions that are not stated in the case will be accepted.

A recent article in USA Today reported that a job awaits 33% of new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At a 99% level of confidence, can we conclude that a larger proportion of students at your school have jobs?

(a) State the null and alternate hypothesis. (b) Determine which distribution to use for the test statistic, and state the level of significance. (c) Calculate the necessary sample test statistics (d) Draw a conclusion and interpret the decision.

NEED ANSWER ASAP

(Hypothesis testing)

What do we need to consider when we try to select a test?

Choose one of the tests; discuss your understandings of that test.

Use some examples to demonstrate your understanding.

NEW ANSWER NEVER USED BEFORE !!!!!!!!!!!!!!!!!

ANSWER THROUGHLY,

COPY AND PASTE PLEASE

John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John.

a. What is the probability that in a given month demand is less than 3,000 units?

b. What is the probability that in a given month demand is greater than 2,200 units?

c. What is the probability that in a given month demand is between 2,200 and 3,000 units?

d. What is the probability that demand will exceed 5,000 units next month?

e. If John wants to make sure that he meets monthly demand with production output at least 95% of the time. What is the minimum he should produce each month?

A company wished to know if the training programme that they developed
for a particular task was effective. 20 employees were timed performing the
task before and after the training. The times were recorded and are given in
Table 1.

Table 1 Time spent performing
the task (in minutes)

Before training After training
27 24
28 23
22 20
26 24
21 21
31 24
29 24
27 23
29 22
29 25
28 23
28 24
28 25
27 22
29 23
28 22
26 23
30 24
26 23
25 22
(a) Enter these data into two lists in Dataplotter.
To check that you have entered the values correctly, the mean number of
minutes that it took to perform the task before training is 27.2 minutes,
and the mean number of minutes it took to perform the task after
training is 23.1 minutes.
Create boxplots for the two datasets, either using Dataplotter or by
hand. Include either a printout of your boxplots or your complete
hand-drawn boxplots with your answer to this question.

(b) A boxplot gives you a visual representation of the average value using
the median, and also tells you how the data are spread out based on
the size of the box and the lengths of the whiskers

(i) How do the average times compare for performing the task before
training and after training? Use your boxplots from part (a) to
explain your answer.

ii) Are the data more spread out for performing the task before
training or after training? Use your boxplots from part (a) to
explain your answer.

(c) Use the boxplot for before training to say whether the data are
symmetrical or skewed. If the data are skewed, then state whether they
are skewed to the left or skewed to the right, explaining your reasoning
briefly.

(d) Create a histogram for each of the datasets, using a start value of 20
and an interval of 1. Include either a printout of your histograms or a
sketch drawn by hand with your answer to this question.

If you draw histograms by hand, then you should use squared paper and
the same axis scale for both histograms to make it easy to compare them.
(e) Comment on one aspect of the time spent performing the task that can
be seen more easily on the histograms than on the boxplots

1.) is there a difference between "2-way Chi-squared" and just "Chi-squared" or are they the same? 2.) How do you find the measurement?

Describe the use of data analytics in business intelligence solutions, including financial, legal, privacy, and ethical issues. Explain how data analytics impact decision making within organizations.

General Electric recently conducted a study to evaluate filaments in their industrial high intensity bulbs. Investigators recorded the number of weeks each high-intensity bulb would last before failure for three test filaments (Groups 1, 2, and 3) and the standard filament (Group 4). The results are as follows. Using ? = 0.01,

Group       1          2       3        4

                 15       14     25     28

                 18       18     19     31

                 21       20     22     27

                 16       16     20     32

                 17       15     18     23

                 20       16     24     25

                18         22     27     30

                              14    18     27     

                                      24     25

                                               26

1. Write an appropriate ANOVA hypothesis to test the difference in means of the four groups (null and alternative).
2. Read the data into R or R-studio, run an ANOVA model in R and paste the code used as well as the output here. What is the decision based on the ANOVA test? You need to explain what part of the output led you to the conclusion you made.
3. Continue using R: Use the Tukey method to test all pairwise contrasts. Show the R code, output, and explain the results of all the comparisons in complete sentences while referencing the parts/numbers on the output that support your conclusions.

WRITE ALL THE CODE USED THE R or R-STUDIO!

1. An IKEA “Tarva” bed frame is assembled with screws and Allen wrenches. The screws and wrenches for the Tarva kits are grabbed at random from large bins at the factory by two different people who never interact. Based on several years of data, it is known that 95% of Tarvas come with the proper size Allen wrenches, and 85% of them come with the correct number of screws. Hints for the two problems below: It may help to write out the list of all possible outcomes of this random process. Also, remember that the probabilities of outcomes add, and that independent probabilities multiply.

   1. (a) The bed frame can only be assembled if it contains the proper size Allen wrench and the correct number of screws. What is the probability that your bed frame can be assembled?

   2. (b) What is the probability that you have either the proper size wrench or the correct number of screws, but not both?

Suppose X is a discrete random variable with mean μ and variance σ^2. Let

Y = X + 1.
(a) Derive E(Y ).

(b) Derive V ar(Y ).

The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can accommodate up to 125 cars and the one on Rio Rancho can accommodate up to 130 cars. City planners are considering both increasing the size of the lots and changing the fee structure. To begin, the Planning Office would like some information on the number of cars in the lots at various times of the day. A junior planner officer is assigned the task of visiting the two lots at random times of the day and evening and counting the number of cars in the lot. The study lasted over a period of one month. Below is the number of cars in the lots for 25 visits of the Ocean Drive lot and 28 visits of the Rio Rancho lot. Assume the population standard deviation is equal and use an alpha value of 0.01 to determine if it is reasonable to conclude that there is a difference in the mean number of cars in the two lots?

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test for this problem? (choose one of the following)

a. t-Test: Paired Two Sample for Means

b. t-Test: Two-Sampled Assuming Equal Variances

c. t-Test: Two-Sample Assuming Unequal Variances

d. z-Test: Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. It is reasonable to conclude that there is a difference in the mean number of cars in the two lots? (choose one of the following) a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

A sample of blood pressure measurements is taken from a data set and those values​ (mm Hg) are listed below. The values are matched so that subjects each have systolic and diastolic measurements. Find the mean and median for each of the two samples and then compare the two sets of results. Are the measures of center the best statistics to use with these​ data? What else might be​ better?

Systolic   Diastolic
154 53
118 51
149 77
120 87
159 74
143 57
152 65
132 78
95 79
123 80

Find the means.
The mean for systolic is__ mm Hg and the mean for diastolic is__ mm Hg.
​(Type integers or decimals rounded to one decimal place as​ needed.)

Find the medians.
The median for systolic is___ mm Hg and the median for diastolic is___mm Hg.
​(Type integers or decimals rounded to one decimal place as​ needed.)

Compare the results. Choose the correct answer below.
A. The mean is lower for the diastolic​ pressure, but the median is lower for the systolic pressure.
B. The median is lower for the diastolic​ pressure, but the mean is lower for the systolic pressure.
C. The mean and the median for the systolic pressure are both lower than the mean and the median for the diastolic pressure.
D. The mean and the median for the diastolic pressure are both lower than the mean and the median for the systolic pressure.
E. The mean and median appear to be roughly the same for both types of blood pressure

Are the measures of center the best statistics to use with these​ data?
A. Since the systolic and diastolic blood pressures measure different​ characteristics, a comparison of the measures of center​ doesn't make sense.
B. Since the sample sizes are​ large, measures of the center would not be a valid way to compare the data sets.
C. Since the sample sizes are​ equal, measures of center are a valid way to compare the data sets.
D. Since the systolic and diastolic blood pressures measure different​ characteristics, only measures of the center should be used to compare the data sets.

What else might be​ better?
A. Because the data are​ matched, it would make more sense to investigate whether there is an association or correlation between the two blood pressures.
B. Because the data are​ matched, it would make more sense to investigate any outliers that do not fit the pattern of the other observations.
C. Since measures of center are​ appropriate, there would not be any better statistic to use in comparing the data sets.
D. Since measures of the center would not be​ appropriate, it would make more sense to talk about the minimum and maximum values for each data set.

1. Suppose we are forming committees within the US Senate. We know there are 100 members and currently there are 48 Democrats and 52 Republicans. Use this information to answer the following. Step 1 of 6: How many committees of 10 Senators can be formed? Round to the nearest million.

what is the probability that a random commitee will contain all democrats?

what is the probability that a random commitee will contain all republicans?

What is the probability that a random committee will contain exactly half Democrats and half Republicans

Interpret your probability from the previous step.

Using your previous answers, which, if any of the committees discussed would be unusual?

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution. 9.3 9.0 10.9 8.5 9.4 9.8 10.0 9.9 11.2 12.1 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.) x = Correct: Your answer is correct. mg/dl s = mg/dl (b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.) lower limit mg/dl upper limit mg/dl