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January 2024 term · Statistics for Data Science I · BSMA1002

Stats 1 End Term: 28 April 2024 (January 2024 term)

The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 28 Apr 2024, in the January 2024 term: 19 questions for 50 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.

Questions
19
Marks
50
Duration
180 min
MCQ
7
MSQ
4
Numerical
8
Take as mock testPractise with answers

Updated

Official paper: IIT M DEGREE AN EXAM QDB3 28 Apr 2024 · No negative marking.

Question 1

+3 marksOne correct option

The probability of a man hitting a target is 1/4. If he fires 5 times, then find the probability that he will hit the target at least twice.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 1 on its own page

Question 2

+2 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • B
  • D
Question 2 on its own page

Question 3

+2 marksOne or more correct options

Choose the correct option(s) from the following.

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 3 on its own page

Question 4

+2 marksOne or more correct options

Which of the following option(s) is/are correct for a variable with interval scale of measurement?

Select all that apply.

  1. A

    Difference between the values of a variable can be evaluated.

  2. B

    Order of the data is meaningful.

  3. C

    Multiplication and division of values of a variable is possible.

  4. D

    It has an absolute zero.

Show answer

Correct answers

  • A

    Difference between the values of a variable can be evaluated.

  • B

    Order of the data is meaningful.

Question 4 on its own page

Question 5

+2 marksOne or more correct options

Which of the following statement(s) is(are) correct?

Select all that apply.

  1. A

    We must preserve the order of an ordinal data in a bar chart.

  2. B

    Mode is not defined for an ordinal data.

  3. C

    Mean can be calculated for a categorical data.

  4. D

    Covariance can be computed only for two numerical variables.

Show answer

Correct answers

  • A

    We must preserve the order of an ordinal data in a bar chart.

  • D

    Covariance can be computed only for two numerical variables.

Question 5 on its own page

Question 6

+3 marksNumerical answer

If the mean of the observations 2a, 10, 3a, 50 and 40 is 30, then find the median of the dataset.

Show answer

Correct answer: 30

Question 6 on its own page

Question 7

+3 marksNumerical answer
Show answer

Correct answer: 3.66 (accepted within ±0.04)

Question 7 on its own page

Question 8

+4 marksNumerical answer

In the first semester of B.S. degree, a student is expected to take 4 subjects. The grades for each subject can be S(10points),A(9points),B(8points),C(7points),D(6points),E(5points) and F(Fail). As per the rules, an enrolled student should obtain a minimum grade E in each subject to get promoted to the next semester. What is the total number of possible ways in which a student can get promoted?

Show answer

Correct answer: 1296

Question 8 on its own page

Question 9

+4 marksNumerical answer

The mean and sample standard deviation of the dataset consisting of 8 observations is 15 and 11 respectively. Later it is noted that one observation 13 is wrongly noted as 10. What is the mean of the original dataset? Enter the answer correct to two decimal places.

Show answer

Correct answer: 15.38 (accepted within ±0.3)

Question 9 on its own page

Question 10

+3 marksOne correct option

In a company, 120 employees are divided into three departments: Marketing, Finance and IT. The number of employees in each department is as follows: 36 in Marketing, 40 in Finance and 44 in IT. An employee, out of 120, is randomly selected for a presentation. Let X denote the number of employees in the department to which that employee belongs. Based on the given information, answer the given subquestions.

Identify the correct distribution of X.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 10 on its own page

Question 11

+2 marksNumerical answer

In a company, 120 employees are divided into three departments: Marketing, Finance and IT. The number of employees in each department is as follows: 36 in Marketing, 40 in Finance and 44 in IT. An employee, out of 120, is randomly selected for a presentation. Let X denote the number of employees in the department to which that employee belongs. Based on the given information, answer the given subquestions.

Find the expected value of X. Enter the answer correct to two decimal places.

Show answer

Correct answer: 40.27 (accepted within ±0.03)

Question 11 on its own page

Question 12

+3 marksNumerical answer

A manufacturing company produces steel rods with lengths between 20 cm and 40 cm. Assume length of steel rods follows a uniform distribution.
Based on the given information, answer the given subquestions.

Show answer

Correct answer: 30

Question 12 on its own page

Question 13

+2 marksOne correct option

A manufacturing company produces steel rods with lengths between 20 cm and 40 cm. Assume length of steel rods follows a uniform distribution.
Based on the given information, answer the given subquestions.

What is the probability that a randomly selected steel rod will have a length of more than 25 cm?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 13 on its own page

Question 14

+2 marksOne correct option

Suppose the time taken by a delivery service to deliver a package (in hours) follows an exponential distribution with a mean delivery time of 10 hours. If someone places an order just before you, then based on the given information, answer the given subquestions.

What is the probability that you will have to wait more than 15 hours for your package to be delivered?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 14 on its own page

Question 15

+3 marksOne correct option

Suppose the time taken by a delivery service to deliver a package (in hours) follows an exponential distribution with a mean delivery time of 10 hours. If someone places an order just before you, then based on the given information, answer the given subquestions.

What is the probability that you will have to wait between 15 hours and 30 hours?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 15 on its own page

Question 16

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Find the value of λ for which 3P(X = 3) = 2P(X = 2) + 4P(X = 1).

  1. A

    2

  2. B

    4

  3. C

    1

  4. D

    −2

Show answer

Correct answer

  • B

    4

Question 16 on its own page

Question 17

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.38 (accepted within ±0.03)

Question 17 on its own page

Question 18

+2 marksOne correct option

Based on the above data, answer the given subquestions.

What is the probability that a patient has the disease and the test is positive?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 18 on its own page

Question 19

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the probability that a patient has the disease given that the test is positive.
Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.42 (accepted within ±0.03)

Question 19 on its own page