Quiz 1

Quantitative Technique (Prof Suranjan Das)

Question 1 - The IQR (Inter Quartile Range) measures the behavior of

Answer - The central 50% of the subjects or respondents

Question 2 - Five different colored crayons are to be distributed amongst nine children. No crayon can be broken. It is true, in certain rounds, some of the children, may or may not get any crayon; they maybe get in other rounds. So what? In how many ways can you distribute crayons?

Answer - Nine to the power of five

Question 3 - Average = 25, Std Dev = 18, Sample size = 36. What is the value of DA at DP more than 22? [Hint: You do not need a laptop or a calculator for this problem. Your mind is more powerful to provide you with the best option from below]

Answer - about 84%

Question 4 - Imagine the Poisson arrival rate of flights to distributed at Terminal 1 with an average of 12 flights per minute (don’t worry, you don’t have to book by sea for your next trip, there are 4 landing strips at Dubai to take such heavy traffic load). What is the probability that upto 8 flights will land in a one minute interval?

Answer - =Poisson (8,12,true)

Question 5 - Imagine that the IQR (Inter Quartile Range) is expressed as a percentage (K%) of the Range of a distribution of ATM withdrawal data. This K% for Emirates Bank (EB) is 70%, while the K% of National Bank of Dubai (NBD) is also 70%. Without making any further assumptions by you, which of the following statements seem to be most appropriate?

Answer - Insufficient information to conclude

Question 6 - The mean and standard deviation of shoe sales per day is $4000 and $800 respectively as given from the main Sharjah outlet of Reebok. At the main Dubai Reebok outlet sales figures given are $6000 and $300 for mean and standard deviation respectively. If both distributions are “Normal”, which of the following statement is most appropriate.

Answer - sales at Sharjah outlet has a higher coefficient of variation (sd/mean) than Dubai outlet

Question 7 - The mean and median of sales per day is $8200 and $7800 respectively as given from the main Paris outlet of Reebok. At the main London Reebok outlet, the same variables are of $9600 and $8600 respectively. Assuming the standard deviation of sales at London is half of that of Paris (but you do not know the actual standard deviation at either place). Which of the following statements is most appropriate:

Answer - Skewness of Paris outlet is less than that of the London outlet

Question 8 - While calculating population standard deviation (not sample standard deviation), we use:

Answer - N in the denominator

Question 9 - The average loss of stock market index per day is 75 (whenever it lost) & std deviation is 18. Data was collected from 36 such trading days when market lost. What will be the probability of getting a loss of, more than 81 points?

Answer - About 2.25%

Question 10 - 5 assignments are to pushed under the cabin door of 2 professors, each of whom are teaching QT-1 and FADM-1 respectively. This can be done in how many ways?

Answer - Insufficient information to conclude

Question 11 - Citibank asked you to refer an enemy of yours, so that they will not send him or her, a credit card. This is an example of

Answer - Snowball sample

Question 12 - 3 assignments in QT-1 and 4 assignments in FADM-1 are to pushed under the cabin doors of 2 professors, each of whom are teaching these QT-1 and FADM-1 courses respectively. This can be done in how many ways?

Answer - 1

Question 13 - The average repair cost of 5 machines is $100 and the average of 10 machines is $250. What is the average of the entire sample of fifteen machines, put together?

Answer - 200

Question 14 - The Central Limit Theorem involves and also emphasizes upon:

Answer - All the other three options

Question 15 - The average gain of stock market index per day is 58 (whenever it gained) & std deviation is 20. Data was collected from 64 such trading days when market gained. What will the z-value be, if we have to find out the market gain of about 16% of the relatively poor gain days?

Answer - 1.0

Question 16 - Data is drawn from a bank on the value of each cheque submitted as deposits from Sunday to Wednesday. Obviously it was a large data set. A distribution of these cheques was generated and the diagram was drawn. The diagram did not have any skew. It means,

Answer - Mean value of cheques and Median value of cheques were same

Question 17 - The average number of flights landing on any day at Dubai is 1200 with a standard deviation of 30 flights. How many flights are expected to land on the busiest 20% of days? Assume there is no sample size given. The result can still be obtained by

Answer - NORMINV(0.80, 1200, 30)

Question 18 - The sum of the squared residual gives an idea of how good the regression model is. This can be established (or ascertained) by

Answer - All three options given (above)

Question 19 - Standard Error is:

Answer - (A) and (B)

Question 20 - Imagine that the IQR (Inter Quartile Range) is expressed as a percentage (J%) of the Range of a distribution of ATM withdrawal amounts. This J% for Emirates Bank (EB) is just 20%, while the J% of National Bank of Dubai (NBD) is 85%. If the Range is same for both banks, and the distributions are “Normal”, which of the following statements is most appropriate?

Answer - Compared to EB, the NBD has more dense clusters or groups, towards its two end points

Question 21 - The mean and median of sales per day is $1200 and $400 respectively as given from the main Delhi outlet of Reebok. At the main Chennai Reebok outlet, the same variables are of $900 and $500 respectively. Assuming the standard deviation of sales at Chennai is three times of that of Delhi (but you do not know the actual standard deviation at either place). Which of the following statements is most appropriate:

Answer - Skewness of Delhi outlet is more than that of the Chennai outlet

Question 22 - In your admission interviews, full mark was, say 500. One professor Tom, has given marks which are ‘+” skew (value ‘+M’) while another professor Jerry, has given marks which are ‘-‘ skew (value ‘–Y’). If selection is made by simply collating data from the two professors… tab to lag jayega.. kaliya (i.e. then it will be real bad). Assume absolute value M is slightly higher than that of Y and the distributions are more or less Normal for both Tom & Jerry. We should then ideally try to (choose the best option)

Answer - Multiply Tom’s marks by a factor “>1” & Jerry’s marks by a factor “<1”, then collate

Question 23 - To get the coefficient of skewness the (Mean – Median) is then

Answer - Divided by one-third of the standard deviation

Question 24 - Descriptive statistics talks about

Answer - Analysis of past data

Question 25 - If a distribution does not give any idea about the base sample size, on which the observed value of the phenomenon is given to us, we can presume, that it perhaps follows a

Answer - Poisson distribution

Question 26 - The mean and median of sales per day is $4000 and $3800 respectively as given from the main Sharjah outlet of Reebok. At the main Dubai Reebok outlet, the same variables are of $6000 and $5300 respectively. Assuming the standard deviation is the same for both outlets, which of the following statements is most appropriate:

Answer - Skewness of Sharjah outlet is less than that of the Dubai outlet

Question 27 - The median of any distribution:

Answer - All the other (above) four propositions

Question 28 - Standard Error:

Answer - (A), (B) and (C)

Question 29 - The average wastage of electricity is 140 MGW per day, standard deviation of 40 MGW. Data was collected from a sample of 40 randomly chosen days in last 5 years. The distribution is Normal. What is the floor value of wastage in MGW for 50% of the highest wastage days?

Answer - 140 MGW

Question 30 - The 4 regions (North, East, West and South) have conveyed to the National Head (Sales) that they all have the same median value of Sales, from their respective dealers in the sale of various grades steel. This indicates that the 4 regions had

Answer - Insufficient information to conclude

Question 31 - At the very broad (preliminary) level, sample can be which of the following two types:

Answer - Probability and non-probability sample

Question 32 - In a distribution that is not Normal distribution, if average = 45, stdev = 45, sample size = 45: and if you are not allowed to apply Standard Error by your client company because they say the sample is the entire market (for their new product)

Answer - None of the other (or, above) options given will be held valid by the company

Question 33 - In a Poisson distribution problem for a bank, if the historical average is set at 6.75 per week, while the decision maker wants to investigate into the possibility of 11 or more over any fortnight, we should ideally

Answer - Scale down the client’s or decision maker’s index, to a week

Question 34 - Binomial distribution is often converted into Normal when

Answer - Historical probability of occurrence is very low and sample size is high

Question 35 - Fifteen out of forty-five parachutes usually open after the critical zone, during an air show as an act of daring display. If the next helicopter drops the remaining 10 paratroopers, what is chance that at least 2 paratroopers will complete d grand air-show? [You do not need laptop, just apply your mind, think of the diagram, the DP, the swanky colors of paratroopers’ dress, visualize these, done time pass, and choose the best answer]

Answer - More than 50%

Question 36 - The number of students in Div-A, whose most favorite course is FADM-1 or QT-1 or GBM are 20, 10 and 30 respectively. The numbers from Div-B incidentally are also 20, 10 and 30 respectively. We want to find out if there is some kind of dependence or connection between most favorite courses chosen and the Divisions. We need to calculate the deviations of the distribution of favorite courses, for each Division, but against the benchmark of entire batch. Once done, the total deviation, derived from the sum of the above deviations, will be

Answer - 0

Sample Paper 1

GMBA Apr_2010 DUBAI
Quantitative Techniques - I (Business Statistics)
End Term Test
Time 90 mins.
Marks 100 Professor:Dr.SuranjanDas
		INSTRUCTIONS BELOW - READ VERY CAREFULLY
Open book, Open notes, Open laptop, Open calculator
NO NETWORK, NO CELL PHONES, NO MOBILE PHONES
Qtn 1 and Qtn 2 - 20 marks each
Qtn 3 to Qtn 6 - 15 marks each
This Question booklet is ALSO your Answer booklet. Submit this when the exam ends
You do not have to submit any Excel file now.
Save your Excel files, we may ask for it later on in case any clarification is needed.
Do not work or save you file after the Exam is over. If you do so, it will not be considered later.
There are 7 pages (Cover plus 6 pages). Please check before starting exam. Report discrepancy, if any
There are 6 questions in 6 different pages.
Marks for each qtn is given on the top of each question.
Answer every question in the same page alotted for it.
If you need more space for a question, use the blank page overleaf, AFTER that question
An electronic copy of data of Qtn 1 & Qtn 2 is available on Blackboard, check with your invigilator
Password (if any) to open this datafile, will be put on your classroom board, just before the exam begins
This datafile will help you save some time, as well as ensure zero mistake, due to data entry error
However, there are other questions where there may be smaller data sets, that you will have to enter
WRONG data entry (& solution) will invite ZERO MARKS, no matter how correctly the problem is done Question 1: (20 Marks) In MNC Pvt Ltd. the following annual data was collected by a Regional Sales Manager (RSM) for the team members under him. The RSM had a few concerns regarding his department. a) He was greatly bothered by the Outstanding Collections (money pending in market) and wanted to design a prediction model. Devise a regression model to help RSM. Assume the RSM believes all other variables (Age, Relevant Experience and Sales (turnover, Salesman wise, in MNC Pvt. Ltd) have got some relation with Outstanding Collections. What is the model? What is the R-sqrd (ignore 'p'-value)? b) The RSM was also considering another task; if he could predict the potential Sales (salesman wise) for a new recruit, 28 yrs old & has about 7 yrs of relevant experience, to whom the RSM has offered the sales job. What will be this model. What is the potential Sales of this new Salesman (ignore 'p'-value)? Age Relev Exp Sales (salesman-wise) Outstanding Collection 25 3 24 23 25 2 35 21 26 4 35 20 26 9 30 19 27 5 34 16 27 8 40 16 29 10 33 13 30 8 43 9 30 12 99 7 31 12 40 6 30 11 52 6 32 10 60 6 34 10 62 5 35 14 55 5 36 13 77 6 37 13 89 4 38 20 112 4 40 12 102 3 45 16 65 1 Find: · Model for (a) · R-Squared · Model for (b) · Sales of New Recruit Question 2: (20 Marks) A certain data of Advertisement Expenses (made) & Sales (obtained) for a company is given below A section of the summary results of a Multiple Regression using this data, is produced below. a) Is/are there any mistake(s) in the results shown? If so, point out b) If the Advt Expense is 11, what would the Sale figure be? c) Using a relevant Statpro analysis, which month will emerge as the least predictable Sale? d) Using a relevant Statpro analysis, which month will emerge as the most predictable Sale? Results of multiple regression for Sales Summary measures Multiple R 0.9612 R-Square 0.9804 StErr of Est 6.1385 Regression coefficients Constant 18.0876 Advt Exp -5.4736

Mention below, the mistake(s) AND ALSO the necessary correction(s)

Question 3: (15 Marks)

Data on handling of containers (by volume, tonnes) at the Dubai shipyard is given by the distribution below. Assume sample is collected from 22,000 containers that berth per year.

Group	Lower limit	Upper limit	No. of Containers in each grp
	(tonnes)	(tonnes)

1	20	30	30
2	30	40	55
3	40	50	100
4	50	60	180
5	60	70	135
6	70	80	60
7	80	90	40

a) What is the mean and standard deviation of volume handled at this shipyard?

b) What is the lower limit of container volume, in tonnes, for the heaviest 15% of containers? (No need to consider Std Error)

c) What is the upper limit of container volume, in tonnes, for the lightest 8% of containers? (No need to consider Std Error)

Question 4: (15 marks)

The average number of customers at the several Pizza Hut stalls in Dubai on Thursday evenings, is 280 with a standard deviation of 95 customers. This information emerged from data collected from 25 randomly chosen Pizza Hut stalls in Dubai. The Pizza Hut management decided to give a special award of AED 15,000 to all Pizza Hut stalls in Dubai, if a "large" proportion of these stalls managed to get a "good" number of customers (by "good" number, they said more than 300 customers) on thursday evenings. By "large' proportion of these stalls, they specified minimum 15% of stalls of Dubai should have reached such "good" number of customers. In other words, if at least 15% of Pizza Hut stalls got "good": numbers (i.e. cross 300 customers), it is an indication Pizza Hut is doing great in Dubai. Will the Pizza Hut stalls in Dubai get this special award & why?

Draw a neat diagram (with axes & appropriate shading of relevant areas) to illustrate, it might help you score (though its not guaranteed), in the event your answer is wrong

Find

· Formula

· Decision

· Reason

· Draw neat diagram and show shaded area and axes

Question 5: (15 marks)

A sample of 15 rodents (captured around our housing colonies like China, Persia and so on) revealed an average of 0.37 mg of harmful toxins that are carried by them with a standard deviation of 0.18 mg. Obviously, these toxins are harmful to human beings; so they have to remain at, as much reduced levels as possible. What is the limit of the level of toxins of rodent samples that you can find, in 20% of the most infected rodent samples in these colonies? Assume, population standard deviation is not known. Give your answer upto 3 decimal places.

Draw a neat diagram (with axes & appropriate shading of relevant areas) to illustrate, it might help you score (though its not guaranteed), in the event your answer is wrong

Find:

· Std Error

· What Distribution

· Value of the test statistic (from table or excel formula)

· Limit

· Draw neat diagram and show shaded area and axes

Question 6: (15 Marks)

If the range of waiting time required to do the immigration at DXB airport is 21 minutes, within which almost the entire bunch (from a sample survey) of passengers normally complete their formalities, and if we know, that the population standard deviation of waiting time at DXB airport is 28 minutes, how many passengers have been considered in the above sample, to arrive at this conclusion?

Draw a neat diagram (with names of axes and appropriate shading of relevant areas) to illustrate. Well, there may be a faint possibility of scoring (though its not guaranteed), in the unfortunate and hopefully unlikely event, of your answer going majorly wayward or funky!

Put your FINAL Answer in the box alongside

Draw neat Diagram (show shaded area & axes)