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Statistics For Economists 1 Cat 1 Question Paper

Statistics For Economists 1 Cat 1

Course:Bachelor Of Economics And Statistics

Institution: Kenyatta University question papers

Exam Year:2010

KENYATTA UNIVERSITY
SCHOOL OF ECONOMICS
DEPARTMENT OF ECONOMETRICS AND STATISTICS

EES 201:STATISTICS FOR ECONOMISTS CAT 1
__________________________________________________________________________________________
INSTRUCTIONS:Answer ALL questions

QUESTION ONE
a)State clearly what is meant by two events being statistically independent..

b)In a certain factory that employs 500 men, 2% of all employees have a minor accident in a given year. Of these, 30% had safety instructions whereas 80% of all employees had no safety instructions.
Required:
Find the probability of an employee being accident-free given that he had:
i)no safety instructions.
ii)safety instructions.

c)An electric utility company has found out that the weekly number of occurrences of lightning striking the transformers is a Poisson distribution with mean 0.4.
Required:
i)The probability that no transformer will be struck in a week.
ii)The probability that at most two transformers will be struck in a week.

QUESTION TWO
a)The past records of Salama Industries indicate that 4 out of 10 of the company’s orders are for export. Further, their records indicate that 48 percent of all orders are for export in one particular quarter. They expect to satisfy about 80 orders in the next financial quarter.
Required:
i)Determine the probability that they will break their previous export record
ii)Explain why you have used the approach you have chosen to solve part (i) above.

b)Grear Tyre Company has just developed a new steel-belted radial tyre that will be sold through a chain of discount stores. Because the tyre is a new product, the company’s management believes that the mileage guarantee offered with the tyre will be an important factor in the consumer acceptance of product. Before finalizing the tyre mileage guarantee policy, the actual road test with the tyres shows that the mean tyre mileage is kilometres and the standard deviation is =5,000 kilometres. In addition, the data collected indicate that a normal distribution is a reasonable assumption.
Required:
i)Grear Tyre Company will distribute the tyres if 20 per cent of the tyres manufactured can be expected to last more than 40,000 kilometers. Should the company distribute the tyres?

ii)The company will provide a discount on a new set of tyres if the mileage on the original tyres does not exceed the mileage stated on the guarantee.

What should the guarantee mileage be if the company wants no more than 10% of the tyres to be eligible for the discount?

c)Explain briefly some of the advantages of the standard normal distribution.

QUESTION THREE
a)In a particular life insurance office, employees Simiyu, Juki, Waithera and Baraza have a diploma, with Simiyu and Baraza also having a degree. Simiyu, Macharia, Waithera, Thuo, Mwanzia and Kungu are associate members of the Chartered Insurance Institute (ACII) with Thuo and Mwanzia having a diploma.
Required:
Identifying set A as those employees with diploma, set C as those employees who are ACII and set D as having a degree:
i)Specify the elements of sets A, C and D.
ii)Draw a Venn diagram representing sets A, C and D, together with their known elements.
iii)What special relationship exists between sets A and D?
iv)Specify the elements of the following sets and for each set, state in words what information is being conveyed: .
v)What will be a suitable universal set for this situation?

b)The purchasing department has analysed the number of orders placed by each of the 5 departments in the company by type of this financial year as given in the table below:

Order type Sales Purchase Production Accounts Maintenance Total
Consumables 10 12 4 8 4 38
Equipment 1 3 9 1 1 15
Special 0 0 4 1 2 7
Total 11 15 17 10 7 60

An error has been found in one of these orders.
Required:
i)Determine the probability that the incorrect order was not for consumables.
ii)Determine the probability that the incorrect order came from maintenance or production.
iii)Calculate the probability that the incorrect order was an equipment order from purchase.

c)
i)Under what conditions does P (A/B) = P (A)?
ii)What is the addition rule of probability and for what type of events is it valid?
iii)What is Bayes Theorem?

QUESTION FOUR
In each of the following three situations, use binomial, poisson, or normal distribution depending on which is the most appropriate.

In each case, explain why you selected the distribution and draw attention to any feature which supports or casts doubt on the choice of distribution.

a)Situation 1:
The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and standard deviation of 160 hours.
Required:
i)Identify situation 1.

ii)If the manufacturer replaces all the components that fail before the guaranteed minimum lifetime of 600 hours, what percentage of the components have to be replaced?

iii)If the manufacturer wishes to replace only 1% of the components that have the shortest life, what value should be used as the guaranteed lifetime?

iv)What is the probability that the mean lifetime of a sample of 25 of these electrical components exceeds 850 hours?

b)Situation 2:
A green grocer buys peaches in large consignments directly from wholesaler. In view of the perishable nature of the commodity, the green grocer accepts that 15% of the supplied peaches will usually be unsaleable. As he cannot check all the peaches individually, he selects a single batch of 10 peaches on which to base his decision of whether to purchase a large consignment or not. If no more than two of these peaches are unsatisfactory, the green grocer purchases the consignment.
Required:
i)Identify situation 2.
ii)Determine the probability that under normal supply conditions, the consignment is purchased.

c)Situation 3:Vehicles pass a certain point on a busy single-lane road at an average rate of two per 10 second interval.
Required:
i)Identify situation 3.
ii)Determine the probability that more than three cars pass this point during a 20 second interval.

QUESTION FIVE
a)Define probability as used in Quantitative Techniques.

b)What is Bayes Theorem? Explain how Bayes Theorem can be utilized practically.

c)KK accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages and 5% show large inventory shortages. KK firm has devised a new accounting test for which it believes the following probabilities hold:
P (Company will pass test/no shortage) = 0.90
P (Company will pass test/small shortage) = 0.50
P (Company will pass test/large shortage) = 0.20

Required:
i)Determine the probability if a company being audited fails this test has large or small inventory shortage.

ii)If a company being audited passes this test, what is the probability of no inventory shortage?

Statistics For Economists 1 Cat 1 Question Paper

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