STAT-201 QUANTITATIVE METHODS (2)

3. Points: Section-I 1×6=6

Section-II 1×6=6

Section-III 6×3=18

Total 30

Section-I

State whether the following statements are True or False. (1×6 = 6)

1. In the equation y = mx+c, y is independent variable.

2. The scatter diagram is generally used to investigate the relationship between variables.

3. First in, First out is not a basic characteristic of a waiting line.

4. A bank with a single queue to move customers to several tellers is an example of a Multi-channel system.

5. In L.P.P objective function is necessary in both maximization and minimization problems.

6. In L.P.P resource restrictions are called constraints.

Section-II

Circle/tick the right answer from the answers given below. (1×6 = 6)

1) The random error is a regression equation

a) is the predicted error

b) includes both the positive and negative terms

c) will sum to a large positive number

d) estimates the accuracy of the slope

2) Which of the following represents the linear model for hypothesis testing

a) y = b0 + b1X + ε

b) y = b0 + b1 + ε

c) y = b0X

d) none of these

3) In queuing theory, the calling population is another name for

a) queue size

b) the servers

c) service rate

d) the arrivals

4) Which of the following is not a valid queuing model based on the Kendall’s notation

a) M/M/0

b) M/M/1

c) M/D/1

d) M/M/m

5) Infeasibility in a L.P.P problem occurs when there is

a) infinite solutions

b) a constraint is redundant

c) there is no solutions that satisfies the given constraint

d) none of these

6) Which of the following is not a part of L.P.P

a) objective function

b) a set of constraints

c) optimization of a linear function

d) a redundant constraint

Section-III

Answer the following Essay Type Questions (6×3=18)

1. In a simple regression model study, the following results are found:

The regression line is 5+2.X

Given and,

.

Calculate SST, SSE, SSR and r2

2. Fit a regression curve to the following data

3. The SEU students open a ticket on “support system” to have solved their university

account problem. Students’ tickets arrival is best described by Poisson distribution with mean of 4 tickets submitted per hour. The support system server can help an average one student in 10 minutes, with the service rate being described by an exponential distribution. Calculate the following characteristics of the service system:

a. The average time a student’s ticket waits in the system.

b. Probability that the system is idle.

4. In Tyson’s mechanic shop customers arrive at the rate of 3 per hour and the Tyson’s mechanic can install wheels at the rate of 6 per hour. Then calculate L ,W and Lq as per M/M/1 model where,

a) L = average no of customers in the system

b) W = average time a customer spends in the system

c) Lq = average no of customers in the queue

5. Susanna Nanna is the production manager for a furniture manufacturing company. The company produces tables and chairs. Each table generates a profit of $80 and requires 4 hours of assembly time and 5 hours of finishing time. Each chair generates $50 of profit and requires 4 hours of assembly time and 3 hours of finishing time. There are 340 hours of assembly time and 250 hours of finishing time available each month. The company must fill an order for 20 tables.

Formulate the problem as a linear program.

6. Using graphical method to solve the Linear Programming Problem

Maximize 𝑍 = 6𝑥 + 7𝑦

Subject to 2𝑥 + 3𝑦 ≤ 12

2𝑥 + 𝑦 ≤ 8

𝑥, 𝑦 ≥ 0

4