GM03
Business Statistics
Assignment No.I
Assignment Code: 2013GM03A1 Last Date of Submission: 15th April 2013
Maximum Marks:100
Attempt all the questions. All the questions are compulsory and carry equal marks.
Section-A
Ques. 1 In a certain examination there were 100 candidates of whom 21 failed, 6 secured
distinctions, 43 were placed in third division and 18 in the second division. It is known that at least 75% marks are required for distinction, at least 40% for passing, at least 50% for second division and at least 60% for first division.
Calculate the median of the distribution of marks
Ques.2 Take any company from the internet or annual report and exhibit the sales and profits for the last five years through graphical representation. Which type of graph in your opinion would be most suitable.
Ques. 3 The standard deviation of a certain population is about 5 units. How large a simple random sample should be if the standard error of the sample mean is to be 1? How large it should be fore the standard error of 0.1?
Ques 4. Distinguish between
(i) Simple Random and Systematic Random method of sampling
(ii) Quartile Deviation and Standard Deviation.
(iii) Probability sampling and Non probability sampling
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.
GM03
Business Statistics
Assignment No.II
Assignment Code: 2013GM03A2 Last Date of Submission: 15th May 2013
Maximum Marks:100
Attempt all the questions. All the questions are compulsory and carry equal marks.
Section-A
Ques. 1 Explain what do you understand by Type I error and Type II error.
Ques .2 A brand manager is concerned that his brand’s share may be unevenly distributed throughout the country. In a survey in which the country was divided into four geographic regions, a random sample of 100 consumers in each region was done and the following were the results. Is the brand manager’s concern justified at 5% level of significance?
REGION
NORTH WEST EAST SOUTH TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Ques.3 A finite population consists of 5 elements: A, B, C, D and E. Enumerate all the possible samples of size 3 that can be drawn from this population. If each of these samples is assigned the probability 1/10, find
(a). the probability that any specific element (say, the element C) will be contained in such a sample
(b). the probability that any specific pair of elements (say, the elements D and E) will be contained in such a sample.
Ques.4 It has been found that 7 per cent of the tools manufactured by a factory are defective. What is the probability that in a shipment of 625 such tools (a) 8 per cent or more, and (b) 7 per cent or less will be defective?
Section-B
Case Study
A firm engaged in manufacturing undergarments for gents employs 100 male and 144 female workers. The average production per day of a male worker is 60 items with a variance of 15 items, and that of a female workers is 65 items with a variance of 12 items. Find the probability
Case Question:
That a sample of 40 females gives an average production which is more than that based on a sample of 36 males by more than 6 items, assuming sampling with replacement, and that, the sample size for the two sexes being the same, the average production of females is more than that of males by less than 6 items, assuming sampling without replacement.
Business Statistics
Assignment No.I
Assignment Code: 2013GM03A1 Last Date of Submission: 15th April 2013
Maximum Marks:100
Attempt all the questions. All the questions are compulsory and carry equal marks.
Section-A
Ques. 1 In a certain examination there were 100 candidates of whom 21 failed, 6 secured
distinctions, 43 were placed in third division and 18 in the second division. It is known that at least 75% marks are required for distinction, at least 40% for passing, at least 50% for second division and at least 60% for first division.
Calculate the median of the distribution of marks
Ques.2 Take any company from the internet or annual report and exhibit the sales and profits for the last five years through graphical representation. Which type of graph in your opinion would be most suitable.
Ques. 3 The standard deviation of a certain population is about 5 units. How large a simple random sample should be if the standard error of the sample mean is to be 1? How large it should be fore the standard error of 0.1?
Ques 4. Distinguish between
(i) Simple Random and Systematic Random method of sampling
(ii) Quartile Deviation and Standard Deviation.
(iii) Probability sampling and Non probability sampling
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.
GM03
Business Statistics
Assignment No.II
Assignment Code: 2013GM03A2 Last Date of Submission: 15th May 2013
Maximum Marks:100
Attempt all the questions. All the questions are compulsory and carry equal marks.
Section-A
Ques. 1 Explain what do you understand by Type I error and Type II error.
Ques .2 A brand manager is concerned that his brand’s share may be unevenly distributed throughout the country. In a survey in which the country was divided into four geographic regions, a random sample of 100 consumers in each region was done and the following were the results. Is the brand manager’s concern justified at 5% level of significance?
REGION
NORTH WEST EAST SOUTH TOTAL
Purchase the brand 40 55 45 50 190
Do not purchase 60 45 55 50 210
Ques.3 A finite population consists of 5 elements: A, B, C, D and E. Enumerate all the possible samples of size 3 that can be drawn from this population. If each of these samples is assigned the probability 1/10, find
(a). the probability that any specific element (say, the element C) will be contained in such a sample
(b). the probability that any specific pair of elements (say, the elements D and E) will be contained in such a sample.
Ques.4 It has been found that 7 per cent of the tools manufactured by a factory are defective. What is the probability that in a shipment of 625 such tools (a) 8 per cent or more, and (b) 7 per cent or less will be defective?
Section-B
Case Study
A firm engaged in manufacturing undergarments for gents employs 100 male and 144 female workers. The average production per day of a male worker is 60 items with a variance of 15 items, and that of a female workers is 65 items with a variance of 12 items. Find the probability
Case Question:
That a sample of 40 females gives an average production which is more than that based on a sample of 36 males by more than 6 items, assuming sampling with replacement, and that, the sample size for the two sexes being the same, the average production of females is more than that of males by less than 6 items, assuming sampling without replacement.
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