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IMT- 24 QUANTITATIVE TECHNIQUE M2

D. Forth Set of Assignments

Two Case Studies : 5 Marks. Each case study carries 2.5 marks.

SECTION – A

1. What are the component of a time series?

2. Assume that the factory has two machines. Past records show that Machine 1 produces 30 per cent of the

output. 5 percent of the items produced by the Machine 1 were defective and only 1 per cent produced by

Machine 2 were defective .If an item selected at random is found to be defective, what is the probability that it

was produced by Machine 2.

3. Gati India Ltd. Maintains Kilometer records on all of its rolling equipment . Here are weekly kilometer records

of its trucks.

810 450 756 789 210 657 589 488 876 689

1450 560 469 890 987 559 788 943 447 775

A) Calculate the median kilometer a truck travelled.

B) Calculate the mean for 20 truck.

C) Compare part (a) and part (b) and explain which one is better measure of central tendency of the data.

4. . Calculate correlation coefficient from the following results:

n=10 ; ∑X=140;∑Y=150

∑(X-10)2

=180; (Y-180)2

∑(X-10)(Y-15)=60

=215

2

5. ABC Builders is engaged in the construction of a multistory building. It has recently conducted a cost audit.

The manger ( cost accounting) has collected the figures of the total cost and its major constituents. The

information collected as percentage of expenditure is shown below. Represent the Data with the help of a

suitable diagram.

Item Expenditure%

Wages

Bricks

Cement

Steel

Wood

Supervision and music

25

15

20

15

10

15

SECTION – B

1. . a) Prove: P(A/B) >P(A),

Then P(B/A)>P(B)

2. What is the probability of obtaining two heads in two throws of a single coin.

3. The two regression coefficients byx and bxy are either both be positive or both be negative. Do you agree

with this statement. If so why ?

4. The equations of two regression lines obtained in a correlation analysis

are given below.

3x + 12y = 19 ; 3y + 9x = 46

obtain (i) the mean values

(ii) the value of correlation coefficient

and (iii) the ratio s x /s y

5. Differentiate between primary data and secondary data. Under what circumstances would secondary data be

more useful than primary data .

SECTION – C

1. Find arithmetic mean, median and mode from the following:

Marks below 10 20 30 40 50 60 70 80

No. of students 15 35 60 84 96 127 198 250

2. A box contains 4 bad and 6 good transistors. Two are drawn out together. One of them is tested and

found to be good. What is the probability that the other one is also good?

On a midterm exam, the scores were distributed normally with mean of 72 and standard deviation of 10.

Student Wright scored in the top 10 percent of the class on the midterm.

3. Wirght’s midterm score was at least how much?

3

4. The final exam also had a normal distribution, but with mean of 150 and standard deviation of 15. At least

what score should Wright get in order to keep the same ranking (i.e , top 10 percent).

5. What do you mean by trend analysis? Differentiate between secular trend and cyclic fluctuation.

CASE STUDY – 1

A restaurant manager has recorded the daily number of customers for the last four weeks. He wants to improve

customer service and change employee scheduling as far as necessary, based on the expected number of daily

customers in the feature. The following data represent the daily number of customers as recorded by the manager for

the last four weeks.

weeks mon Tues wed thurs fri sat sun

1

2

3

4

440

510

490

500

400

430

580

500

480

500

410

470

510

520

630

540

650

740

720

780

800

850

810

900

710

800

690

850

Determine the daily seasonal indices using the seven day moving average.

CASE STUDY – 2

A batch of 5000 electric lamps have a mean life of 1000 hours and standard deviation of 75 hours. Assume a normal

distribution.

a. How many lamps will fail before 900 hours?

b. How many lamps will fail between 950 and 1000 hours?

c. What proportion of lamps will fail before 925 hours?

d. Given the same mean life , what would the standard deviation have to be ensure that no more than 20% of

lamps fail before 916 hours?

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