GM 03
Business Statistics
Assignment I
Assignment Code: 2012 GM03 B1 Last Date of Submission: 15th October, 2012
Maximum Marks: 100
Attempt all the questions. All questions are compulsory and carry equal marks
SECTION – A
1. a) Distinguish between discrete and continuous probability distribution.
b) A dart player throws is given ten attempts to hit the bulls eye. He is had good practice and believes that he will be able to hit the bulls eye 90% of the time. What is the probability that he will have hit the bulls eye at least 6 times. State the assumptions you make while answering this question.
2. a) A batch of products is produced using two machines namely M1 and M2. It is believed that 30% of the products are produced using machine 1. Each machine is unable to produce all items which can be accepted. Hence Machine 1 produces only 94% of the products that can be accepted and machine 2 produces 98% of the products which can be accepted. One piece of the product is taken at random from the whole lot of production and is found to be defective. Find the probability that the defective piece found was produced by Machine 1.
b)It is found that a story book containing 200 pages contained on an average 2 spelling mistakes in every 10 pages. What is the probability that in the next 25 pages of the book that you read there will be more than 8 spelling mistakes. What is the expected number of spelling mistakes per 25pages and the variance in the spelling mistakes per 25 pages.
3. A company has given a contract to a bottling plant to fill its products with the product. The company has specified to the bottling plant that not more than 1% of the bottles should contain less than 980 ml of the product.
a. Find the mean fill rate that the bottling plant must set so as to maintain the guideline stated by the company. The standard deviation is believed to be 40 ml per bottle.
b. The bottling plant has also found that it can install a machine which will reduce the standard deviation from 40ml to 10ml, but this needs to be replaced after filling 50000 bottles and it costs the company Rs. 30000. Each bottle of 1000 ml is sold to the company for Rs. 10. Should the bottling plant install this new machine ?
4. The GMAT scores of students who are potential applicants to a university are normally distributed with a mean of 487 and a standard deviation of 98.
i. What percentage of students will have scores exceeding 500?
ii. What percentage of students will have scores between 600 and 700?
iii. If the university wants only the top 75% of the students to be eligible to apply, what should be the minimum GMAT score specified for eligibility?
iv. Find the narrowest interval that will contain 75% of the students’ scores.
Find x such that the interval [x,2x] will contain 75% of the students’ scores. (There are two answers. See if you can find them both.)
SECTION- B
A Company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Factors such as vibration, temperature, and wear and tear affect the pins, so that the lengths of the pins made by the machine are normally distributed with a mean of 1.008 inches and a standard deviation of 0.045 inches. The company supplies the pins in large batches to a customer. The customer will take a random sample of 50 pins from the batch and compute the sample mean. If the sample mean is within the interval 1.000 ± 0.010 inch, then the customer will buy the whole batch.
1. Find the probability that a batch will be acceptable to the consumer?
2. If you were the manager of the company would be satisfied with the above level of probability and if not what would you think should be reasonable level of probability.
3. If the lathe can be adjusted to have the mean length at any desired value, what should it be adjusted to achieve the probability you desire in part (2) above.
GM 03
Business Statistics
Assignment II
Assignment Code: 2012 GM03 B2 Last Date of Submission: 15th November 2012
Maximum Marks: 100
Attempt all the questions. All questions are compulsory and carry equal marks.
SECTION – A
1. a) Explain the need for different forecasting techniques. How can we evaluate as to how good is
our forecast.
b) Collect data on the amount of expenditure you do each day for the next 25 days and based on the same forecast using 7day moving average the forecast for the 26th day. Evaluate the accuracy of your forecast.
c) Explain one application where you can apply Queuing Theory in daily life.
2. Customers from the Higher Income Group were sampled to test the quality of foods at one of the four major restaurant run by the Taj Group of Hotels. The four types of foods for which the quality were to be checked were Chicken Platter, Honey Chicken, Chicken Spinach, and Tandoori Chicken. Each of the respondent were asked to rate in a scale of 1- 10. The following were the data.
Chicken Platter Honey Chicken Chicken Spinach Tandoori Chicken
6 8 7 6
7 8 6 6
8 9 6 7
5 8 6 6
9 7 5 8
8 9 7 7
7 8 7 6
Is there sufficient evidence to indicate that the quality of food being served is different. Use 5% level of significance.
3. Maxwell’s Hot Chocolate is concerned about the effect of the recent year long coffee advertising campaign on hot chocolate sales. The average weekly hot chocolate sales two years ago was 984.7 pounds and the standard deviation was 72.6 pounds. Maxwell’s has randomly selected 30 weeks from the past year and found average sales of 912.1 pounds.
1. State appropriate hypotheses for testing weather hot chocolate sales have decreased.
2. At the 2 percent significance level, test the hypotheses.
4. A manufacturer was making sport shirts for men. The manufacturer was mainly catering to the needs of Baseball, Basketball, and Football players. Their salesman had given a feedback to the company that the games for which the firm wanted to cater was equally applicable for both men and women and hence recommended that the firm should start making sport shirts for women as well. The firm collected data which are as follows:
Gender Baseball Basketball Football
Men 19 15 24
Women 16 18 16
Does the data suggest whether the requirement is gender specific at 5% level of significance
SECTION-B
The debt-to-capital ratio of a company signifies the amount of financial risk a company is taking. If the ratio is high, the risk is high. This is because when the profit margin falls, debt will worsen the situation by making the return on capital fall even more adversely. The data on debt-to-capital ratio and return on capital for 12 different health care companies were collected and given in table below. Assume that this is a random sample of health care companies. Carry out a Regression analysis on the data for return on capital against debt-to-capital ratio and then answer the following questions.
1. What is the regression equation. (3)
2. Construct the ANOVA table and check the significance level of the regression model.
3. Calculate the coefficient of correlation and test its significance at 5% level of significance.
Company Debt/Capital ( %) Return on Capital ( %)
Abbott Laboratories 11 31
Allergan 24 25
Cardinal Health 30 14
Johnson & Johnson 11 25
Eli Lilly 31 40
Merck 15 33
Pfizer 7 23
SmithKline Beecham 10 22
Bristol-Myers Squibb 12 45
Stryker 55 14
United Health 10 17
Universal Health 38.6 9.8
Business Statistics
Assignment I
Assignment Code: 2012 GM03 B1 Last Date of Submission: 15th October, 2012
Maximum Marks: 100
Attempt all the questions. All questions are compulsory and carry equal marks
SECTION – A
1. a) Distinguish between discrete and continuous probability distribution.
b) A dart player throws is given ten attempts to hit the bulls eye. He is had good practice and believes that he will be able to hit the bulls eye 90% of the time. What is the probability that he will have hit the bulls eye at least 6 times. State the assumptions you make while answering this question.
2. a) A batch of products is produced using two machines namely M1 and M2. It is believed that 30% of the products are produced using machine 1. Each machine is unable to produce all items which can be accepted. Hence Machine 1 produces only 94% of the products that can be accepted and machine 2 produces 98% of the products which can be accepted. One piece of the product is taken at random from the whole lot of production and is found to be defective. Find the probability that the defective piece found was produced by Machine 1.
b)It is found that a story book containing 200 pages contained on an average 2 spelling mistakes in every 10 pages. What is the probability that in the next 25 pages of the book that you read there will be more than 8 spelling mistakes. What is the expected number of spelling mistakes per 25pages and the variance in the spelling mistakes per 25 pages.
3. A company has given a contract to a bottling plant to fill its products with the product. The company has specified to the bottling plant that not more than 1% of the bottles should contain less than 980 ml of the product.
a. Find the mean fill rate that the bottling plant must set so as to maintain the guideline stated by the company. The standard deviation is believed to be 40 ml per bottle.
b. The bottling plant has also found that it can install a machine which will reduce the standard deviation from 40ml to 10ml, but this needs to be replaced after filling 50000 bottles and it costs the company Rs. 30000. Each bottle of 1000 ml is sold to the company for Rs. 10. Should the bottling plant install this new machine ?
4. The GMAT scores of students who are potential applicants to a university are normally distributed with a mean of 487 and a standard deviation of 98.
i. What percentage of students will have scores exceeding 500?
ii. What percentage of students will have scores between 600 and 700?
iii. If the university wants only the top 75% of the students to be eligible to apply, what should be the minimum GMAT score specified for eligibility?
iv. Find the narrowest interval that will contain 75% of the students’ scores.
Find x such that the interval [x,2x] will contain 75% of the students’ scores. (There are two answers. See if you can find them both.)
SECTION- B
A Company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Factors such as vibration, temperature, and wear and tear affect the pins, so that the lengths of the pins made by the machine are normally distributed with a mean of 1.008 inches and a standard deviation of 0.045 inches. The company supplies the pins in large batches to a customer. The customer will take a random sample of 50 pins from the batch and compute the sample mean. If the sample mean is within the interval 1.000 ± 0.010 inch, then the customer will buy the whole batch.
1. Find the probability that a batch will be acceptable to the consumer?
2. If you were the manager of the company would be satisfied with the above level of probability and if not what would you think should be reasonable level of probability.
3. If the lathe can be adjusted to have the mean length at any desired value, what should it be adjusted to achieve the probability you desire in part (2) above.
GM 03
Business Statistics
Assignment II
Assignment Code: 2012 GM03 B2 Last Date of Submission: 15th November 2012
Maximum Marks: 100
Attempt all the questions. All questions are compulsory and carry equal marks.
SECTION – A
1. a) Explain the need for different forecasting techniques. How can we evaluate as to how good is
our forecast.
b) Collect data on the amount of expenditure you do each day for the next 25 days and based on the same forecast using 7day moving average the forecast for the 26th day. Evaluate the accuracy of your forecast.
c) Explain one application where you can apply Queuing Theory in daily life.
2. Customers from the Higher Income Group were sampled to test the quality of foods at one of the four major restaurant run by the Taj Group of Hotels. The four types of foods for which the quality were to be checked were Chicken Platter, Honey Chicken, Chicken Spinach, and Tandoori Chicken. Each of the respondent were asked to rate in a scale of 1- 10. The following were the data.
Chicken Platter Honey Chicken Chicken Spinach Tandoori Chicken
6 8 7 6
7 8 6 6
8 9 6 7
5 8 6 6
9 7 5 8
8 9 7 7
7 8 7 6
Is there sufficient evidence to indicate that the quality of food being served is different. Use 5% level of significance.
3. Maxwell’s Hot Chocolate is concerned about the effect of the recent year long coffee advertising campaign on hot chocolate sales. The average weekly hot chocolate sales two years ago was 984.7 pounds and the standard deviation was 72.6 pounds. Maxwell’s has randomly selected 30 weeks from the past year and found average sales of 912.1 pounds.
1. State appropriate hypotheses for testing weather hot chocolate sales have decreased.
2. At the 2 percent significance level, test the hypotheses.
4. A manufacturer was making sport shirts for men. The manufacturer was mainly catering to the needs of Baseball, Basketball, and Football players. Their salesman had given a feedback to the company that the games for which the firm wanted to cater was equally applicable for both men and women and hence recommended that the firm should start making sport shirts for women as well. The firm collected data which are as follows:
Gender Baseball Basketball Football
Men 19 15 24
Women 16 18 16
Does the data suggest whether the requirement is gender specific at 5% level of significance
SECTION-B
The debt-to-capital ratio of a company signifies the amount of financial risk a company is taking. If the ratio is high, the risk is high. This is because when the profit margin falls, debt will worsen the situation by making the return on capital fall even more adversely. The data on debt-to-capital ratio and return on capital for 12 different health care companies were collected and given in table below. Assume that this is a random sample of health care companies. Carry out a Regression analysis on the data for return on capital against debt-to-capital ratio and then answer the following questions.
1. What is the regression equation. (3)
2. Construct the ANOVA table and check the significance level of the regression model.
3. Calculate the coefficient of correlation and test its significance at 5% level of significance.
Company Debt/Capital ( %) Return on Capital ( %)
Abbott Laboratories 11 31
Allergan 24 25
Cardinal Health 30 14
Johnson & Johnson 11 25
Eli Lilly 31 40
Merck 15 33
Pfizer 7 23
SmithKline Beecham 10 22
Bristol-Myers Squibb 12 45
Stryker 55 14
United Health 10 17
Universal Health 38.6 9.8
No comments:
Post a Comment