Quantitative Methods for Decision Making Assignment -
Q1. A market research organisation has observed that out of 10000 employees, only 200 can stay with the same company for at least 5 years if the candidate has a doctoral qualification. With growing competition worldwide, everyone wants to hire skilled professionals. The executives of a certain financial organization want to decide the expected number of people with a doctoral qualification to stay with their company for next 5 years or more if they hire 30 people.
a) State the probability distribution you use.
b) Write down the probability mass function (p.m.f.) of that distribution. (Remember to put the range of the random variable.)
c) Calculate the expected number of people as required.
d) What is the probability that out of 30 hired professional, less than 5 will continue for 5 years or more?
Q2. Money transaction in a certain ATM occurs at a rate of 3 per hour during 11 hrs. of daytime, from 06.00 am to 05.00 pm. A bank wants to know the following probabilities to decide if another ATM should be opened nearby. Analysts of that bank know the arrival of customers at an ATM can be modelled by a Poisson distribution.
a) What is the average number of people to use the ATM during 11 hrs. between 06.00 am to 05.00 pm?
b) Suppose the rate of arrival of customers at that ATM is 0.5 during 13 hrs. between 05:00 p.m. to 06:00 a.m. What is Average number of people to use that ATM in 24 hrs.?
c) What is the probability that more than 30 people will use that ATM during the daytime.?
d) What is the probability that more than 30 people will use the ATM in 24 hrs.?
Q3. An insurance company fits a normal distribution to the lifetime of a car before it hits an accident in a certain city. Suppose the lifetime of a car follows a normal distribution with mean 10 years and standard deviation 1 years. Find the probability that,
a) A car will not hit any accident for next 15 years?
b) Decide the timespan so that the probability that a car will hit an accident in that city is less than 0.00001?
Q4. Suppose the sale of new cars of a certain brand in that city is 1,00,00,000 per year. Price of a new car is 200,000 Rs. The company decides to insure a new car for 5 years for full replacement for any accidental damage.
a) Calculate the probability that a car will hit an accident in less than 5 years assuming normal distribution with mean 10 and standard deviation 1.
b) Based on this probability, calculate the expected number of cars to fall in an accident in first 5 years. Then calculate the expected pay-out for the company for every 1,00,00,000 newly purchased cars.
c) The probability of getting a new car insured is 0.1, i.e., in every 10 people 1 can insure the car. The company decides to keep 100 Rs. yearly premium for every insured car. Calculate the expected profit for the company after 5 years.
Q5. Suppose the annual maintenance cost of a certain office is normally distributed with standard deviation is Rs. 625 (in lacs). But the mean is not known. The distribution of maintenance cost is assumed to be normal.
a) What is the mean of the distribution if 75% of maintenance cost is more than 1700 Rs. (in lacs)?
b) Using that mean and standard deviation, obtain the probability of maintenance cost for any year to exceed Rs. 3000 (in lacs)?
Project -
Instruction: Project report should not be more than two A4 pages.
A market research firm wants to study if the sales of a certain brand of outfit differs significantly during Diwali in five megacities.
They arranged a survey over the country by randomly choosing a few shops/showrooms in each megacity. Some shop owners denied providing any feedback. So, the observed dataset does not have same number of observations for every city.
The dataset is as follows.
Table 1. Sales (in millions) figures from a number of shops/showrooms for five different cities.
|
Delhi
|
Mumbai
|
Chennai
|
Kolkata
|
Bengaluru
|
|
16.42
|
17.48
|
17.87
|
17.67
|
21.20
|
|
15.29
|
19.69
|
17.85
|
17.05
|
18.85
|
|
17.76
|
20.01
|
14.07
|
19.53
|
23.46
|
|
16.40
|
19.37
|
24.49
|
15.50
|
15.20
|
|
16.11
|
12.69
|
22.85
|
18.58
|
17.92
|
|
17.65
|
19.82
|
15.45
|
18.51
|
18.03
|
|
17.34
|
16.14
|
16.34
|
20.02
|
16.18
|
|
18.18
|
23.42
|
22.92
|
16.46
|
17.76
|
|
18.17
|
17.56
|
23.88
|
22.43
|
17.28
|
|
16.18
|
14.48
|
17.18
|
17.53
|
20.44
|
|
|
14.51
|
14.44
|
15.36
|
18.17
|
|
|
13.49
|
20.90
|
11.38
|
14.43
|
|
|
18.96
|
21.01
|
21.69
|
19.83
|
|
|
10.48
|
22.02
|
18.50
|
|
|
|
21.77
|
17.15
|
|
|
Conduct a detail one-way ANOVA study. Write down the objective of the study, then construct the null and alternate hypothesis, identify dependent and independent variable(s) with reason, prepare the ANOVA table with detail calculation and report your findings in very detail. Then state the conclusion you can draw.
Attachment:- Assignment Files.rar