Indian Institute of Management Bangalore

QM105: Quantitative Methods IQuiz 1

Time: 1 hour 15 minutes Name:___________________

Max Points: 20 Roll No.:_________________

This is an open-book, open note exam; however you are not allowed to share material with other students. Use of calculator is permitted, but not computer (laptop). Do not seek any clarifications.

Do not attach any additional sheets; use the back sides, if necessary.

To get any credit, you must

circle/clearly indicate your final answer (in the space, whenever provided);

answer all questions in the space provided,

show (brief) adequate reasoning, including calculations, if any, in support of your answers.

State any assumption you make. (Your assumptions need to be reasonable.)

This test + answer booklet has 8 pages, including this page.

Space for evaluation only

Question No. 1 2 3 Total

Maximum Marks 1+2+1+2=6 2+2+2=6 (1+3+2)+1+1=8 20

Student’s Score

Page 1 of 5

Question 1. The descriptive statistics tool for current ratio of a group of companies yields the following output, which is partially shown:

Current Ratio  

Median 1.67Mode 1.36Sample Variance 0.49Kurtosis 2.6Skewness 1.73Minimum 0.61Maximum 6.74Sum 363Count 180Largest(45) 3.36Smallest(45) 0.92

a) What is the mean current ratio of the selected companies?

[1 point]

b) Name and compute two different measures of (absolute) dispersion (other than variance, which is already included in the table), for current ratio of the selected companies?

[2 points]

Page 2 of 5

c) What can you say regarding skewness and kurtosis of the distribution of current ratio of these companies? Use appropriate terminologies to describe these.

[1 point]

d) What best can you say regarding the number of companies in this list which has current ratio more than 3.25?

[2 points]

Page 3 of 5

Question 2.

Students in a business school have to become a member of one and exactly one of the following 3 clubs:

Party club (they would attend the Sunday night parties from 10 pm till 2 am) Sleeping club (they would sleep through this time) Study club (they would be studying during this time)

Before the new students enroll for the clubs, the new Dean has asked the students’ committee to truthfully put up the chances of missing next day’s class, getting A grade, getting one of the failing grades (D or F) for each of the 3 club members, based on the past data. (The school gives letter grades in the form A/B/C/D/F. ) Accordingly, the notice board in students’ canteen, has this notice:

Probability of

Club Missing class

Getting A grade

Getting D or F grade

Sleeping

0.050.2 0.05

Party 0.2 0.05 0.1Study 0.1 0.4 0.02

Only 60% of the new batch signs up for the Party club, while the membership for the Study club is 3 times as strong as the membership of the Sleeping club.

a) What would be the percentage of B and C grades (combined) for the new batch of students?

[2 points]

b) Given that a student got a failing grade (D or F), what is chance that he is a member of Party club?

[2 points]

c) If there are 150 students in the new batch, what is the chance that more than 1 member of the Sleeping club from this batch will miss the class the next day?

[2 points]

Question 3.

A tennis match is composed of a number of sets. A set consists of games, and games, in turn, consist of points.

A game consists of a sequence of points. Any point played always results in favour of either the server (who starts the play of that point) or the receiver (opponent of the server). A game is won by the first player to have won at least four points in total and at least two points more than the opponent.

Page 4 of 5

Because of these rules, the number of points to be played before a game is won can vary from a game to another. The game is said to yield to at least one deuce, if the number of points in that game is more than 6. [Denoting 1 by player 1 winning a point, 2 by player 2 winning the point, the following are some examples of how a game can end: 11121, or 1221121222 or 12221111 ---in the first example, there is no deuce]

During one particular game, for any of the points played, the player named F has 70% chance of winning the point vs. his opponent R.

a) Find the probability distribution of the number of points played in the game. Listing the possible values of the random variable along with finding the (non-zero) probabilities associated with at least 4 different values of this random variable would suffice. [Hint: you may find it convenient to split into cases when F wins the game and the cases when R wins]

[1+5= 6 points]

Space for working 3 a)

b) What can you say regarding the chance of F winning the game? (A good lower bound would suffice)

[1point]

c) What is the chance of F winning the game if the game is won before any deuce?

[1point]

Page 5 of 5