ism-2003-quiz1

8/3/2019 ISM-2003-Quiz1

http://slidepdf.com/reader/full/ism-2003-quiz1 1/4

Indian Institute of Management Bangalore

PGP 2003-05

Introduction to Statistical Methods: QMM 101

Quiz 1

Name:___________________ Time: 1 hour

Max Points: 15 Roll No.:_________________

This is an open-book and open-note test.

However, sharing of material is NOT permitted.

Instructions: Do not seek any clarifications. Provide appropriate arguments and show

calculation in support of your final answer. Answer all questions in the space

provided. Do not attach any additional sheets , use the back pages, if necessary.

Question I (9 points)

Subbu has recently joined Swetha Unlimited Services India (Ltd) also known as SUSIL.

SUSIL is a major service provider to many software companies in Bangalore. SUSIL

handles the salary payments as well as the salary deductions to the employees of the

software companies. They also have to handle the complaints received from theemployees. Subbu is one of the “complaint handlers” specially designated to handle the

complaints of the employees of Indosys Pvt Ltd. The number of complaints that he

handles in a day is random but on average, he handles 8 complaints per day.

SUSIL, based on their contract with Indosys, pays Subbu according to his performance.

His performance is rated as “Low”, if he handles 5 or less number of complaints in a day.His performance is rated as “Par” if he handles 6 to 10 complaints in a day and

“Excellent” if he handles more than 10 complaints in a day. He is paid Rs. 200 per a

“Low” day, Rs. 300 per a “Par” day and Rs. 600 per an “Excellent” day. Subbu feels this

is somewhat unfair, since the arrival of complaints is a random process over which he hasno control. However, he has little choice in the matter.

1. On a particular day selected at random, what is the probability that Subbu is paid Rs. 600?

8/3/2019 ISM-2003-Quiz1


2. In a 5-day week, what is the probability that Subbu has 3 “Low” days?

3. What is the average amount received by Subbu in a 5-day week?

4. SUSIL offered to shift Subbu from Indosys to Sikai Technologies. He has to

shift in the beginning of next week. Subbu decided to take advantage of thisopportunity to take a few days off this week. He decided that the moment his

total earnings for the week equaled or exceeded Rs.600, he would take the rest

of the week off. Consider the number of days that Subbu takes leave as arandom variable. What is the probability distribution of this random variable?

Assume it is Monday morning and the first day of the 5-day week.

8/3/2019 ISM-2003-Quiz1


5. As per the contract with Sikai Technologies, Subbu will be paid a lump sum

of Rs. 150 per day (irrespective of the number of complaints handled by him)

and an additional commission of Rs. 20 for every complaint handled by him.Should he shift to Sikai Technologies or remain with Indosys? Justify your

answer appropriately.

Question II (6 Points)

Sarin played a large number of one-day cricket matches for the home team and he alwayscame in to bat at number three. As in the case of many other players, it was felt that his

performance was not very consistent. His coach analyzed his batting and found a veryinteresting pattern. He found that Sarin came in to bat in the early overs (first 16 overs)

50% of the time; in the middle overs (between 17th and 33rd overs) 20% of the time and in

the last overs (last 17 overs) 30% of the time. The number of runs that he scored in all

the three situations was normally distributed with a mean of 40 runs. But, the variancehas been different in the three situations: 100 runs2 in the early overs; 64 runs2 in the

middle overs and 25 runs2 in the last overs.

1. What is the probability that Sarin scores 50 or more runs if he comes to bat in the

early overs?

2. What is the probability that he scores 50 or more runs?

8/3/2019 ISM-2003-Quiz1


3. What is the probability that he scores 50 or more runs in 3 consecutive matches?

(Clearly state any assumptions that you have to make)

4. When do you suggest that Sarin should be brought in for batting, early overs,

middle overs or last overs?

ism-2003-quiz1

Documents