The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 11 Dec 2022, in the September 2022 term, set ETF1: 14 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Which of the following statement(s) is/are incorrect?
Descriptive statistics can be performed only on population data.
Inferential statistics can be performed on both population data and sample data.
Descriptive statistics can be performed on both population data and sample data.
Inferential statistics cannot be performed on population data.
Correct answers
Descriptive statistics can be performed only on population data.
Inferential statistics can be performed on both population data and sample data.
Correct answer: 2
Correct answer: 0.6 (accepted within ±0.05)
Samsung mobile company launched two new phones, Galaxy A03 and Galaxy S22. The probability that Galaxy A03 has good battery life is 60% and the probability that Galaxy S22 has good battery life is 80%. If a phone is selected randomly, then what is the probability that it has a good battery life? (Enter the answer correct to 2 decimal accuracy).
Correct answer: 0.7 (accepted within ±0.05)
Consider the experiment of selecting a three-child family at random. If ‘b’ denotes of being a boy and ‘g’ denotes of being a girl, then find the possible values of the event “The first born is a boy”?
Correct answer
If X and Y are independent Poisson random variables with expectations 5 and 3 respectively, then find the variance of 2X + Y .
17
13
23
Insufficient information
Correct answer
23
0
1
2
3
Correct answer
3
The difference between the number of ways n distinct letters can be arranged with repetition and without repetition is 21. Find the value of n.
4
3
5
Insufficient information.
Correct answer
3
Consider the dataset 15, 19, 12, 21 and 17. If we add 4 to all observations, then what is the difference between 75*^(th)* percentile of new dataset and 50*^(th)* percentile of old dataset?
2
6
7
4
Correct answer
6
An owner of a television shop sends his repairman to service five televisions on site each day. It is found that half of the service calls require installation of a particular part in the television. If the repairman has only one such part, then find the probability that at most one television he services will require installation of this particular part.
(Enter the answer correct to 3 decimal accuracy.)
Correct answer: 0.188 (accepted within ±0.005)
The amount of time that a particular machine can run before its battery wears out is exponentially distributed with an average of 100 hours. The owner of the factory needs to run that machine more than 50 hours to complete a deal with company-A. Based on the information , answer the given subquestions
Hint: e = 2.718
What is the probability that he will be able to complete the deal with company-A without having to replace the machine battery? (Enter the answer correct to 3 decimal accuracy)
Correct answer: 0.607 (accepted within ±0.005)
The amount of time that a particular machine can run before its battery wears out is exponentially distributed with an average of 100 hours. The owner of the factory needs to run that machine more than 50 hours to complete a deal with company-A. Based on the information , answer the given subquestions
Hint: e = 2.718
If the owner has already used the machine for more than 40 hours to complete the previous orders, then what is the probability that he will be able to complete the deal with company-A without having to replace the machine battery? (Enter the answer correct to 3 decimal accuracy)
Correct answer: 0.607 (accepted within ±0.005)
The time that buses will reach on a particular stand inside IIT Madras campus is uniformly distributed between a minutes and 30 minutes. If the 90*^(th)* percentile for the bus time to reach on a bus stand is 29 minutes, then based on the information, answer the given subquestions
Find the value of a.
Correct answer: 20
The time that buses will reach on a particular stand inside IIT Madras campus is uniformly distributed between a minutes and 30 minutes. If the 90*^(th)* percentile for the bus time to reach on a bus stand is 29 minutes, then based on the information, answer the given subquestions
Find the expected time taken by buses to reach on a particular stand inside IIT Madras campus.
Correct answer: 25
