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May 2024 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 2: 4 August 2024 (May 2024 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 4 Aug 2024, in the May 2024 term: 16 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
16
Marks
40
Duration
120 min
MCQ
8
Numerical
7
MSQ
1
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN EXAM QDD2 4 Aug 2024 · No negative marking.

Question 1

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 1 on its own page

Question 2

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 2 on its own page

Question 3

+3 marksOne correct option

A political survey is conducted to estimate the proportion of voters in a city who support a particular candidate. The true proportion of voters supporting the candidate is 0.45. A random sample of 500 voters is taken. Using Central limit theorem, what is the approximate probability that the sample proportion is between 0.43 and 0.47?

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

Correct answer

  • D
Question 3 on its own page

Question 4

+3 marksNumerical answer
Show answer

Correct answer: 5

Question 4 on its own page

Question 5

+1 markNumerical answer

Based on the above data answer the given subquestions.

Show answer

Correct answer: 0.11 (accepted within ±0.02)

Question 5 on its own page

Question 6

+2 marksOne or more correct options

Based on the above data answer the given subquestions.

Which among the following options are true?

Select all that apply.

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

Correct answers

  • B
  • C
Question 6 on its own page

Question 7

+3 marksOne correct option

Based on the above data answer the given subquestions.

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

Correct answer

  • B
Question 7 on its own page

Question 8

+2 marksNumerical answer

Based on the above data answer the given subquestions.

Show answer

Correct answer: 1

Question 8 on its own page

Question 9

+2 marksNumerical answer

A survey reports that the average time spent on social media per day by teenagers is 3 hours, with a standard deviation of 1 hour. A researcher selects a random sample of 64 teenagers. Based on the above data answer the given subquestions.

What is the expected value of the sample mean time spent on social media?

Show answer

Correct answer: 3

Question 9 on its own page

Question 10

+3 marksOne correct option

A survey reports that the average time spent on social media per day by teenagers is 3 hours, with a standard deviation of 1 hour. A researcher selects a random sample of 64 teenagers. Based on the above data answer the given subquestions.

Using Chebyshev’s inequality, find the least upper bound on the probability that the sample mean time deviates from the population mean time by more than 0.5 hours.

  1. A

    0.0625

  2. B

    0.9375

  3. C

    0.031

  4. D

    0.015

Show answer

Correct answer

  • A

    0.0625

Question 10 on its own page

Question 11

+2 marksOne correct option

The recovery time for a particular surgery in a hospital follows an exponential distribution with a mean of 5 days. A researcher collects data from a sample of 49 patients.
Based on the above data answer the given subquestions.

Using CLT, what will be the approximate distribution of the sample mean recovery time?

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

Correct answer

  • B
Question 11 on its own page

Question 12

+3 marksNumerical answer

The recovery time for a particular surgery in a hospital follows an exponential distribution with a mean of 5 days. A researcher collects data from a sample of 49 patients.
Based on the above data answer the given subquestions.

Using CLT, what is the approximate probability that the sample mean recovery time is between 4 and 6 days? Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.84 (accepted within ±0.02)

Question 12 on its own page

Question 13

+3 marksOne correct option

Based on the above data answer the given subquestions.

What is the distribution of X?

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

Correct answer

  • C
Question 13 on its own page

Question 14

+2 marksNumerical answer

Based on the above data answer the given subquestions.

Find the conditional probability P(W = 1 | X = −1). Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.12 (accepted within ±0.02)

Question 14 on its own page

Question 15

+2 marksNumerical answer

Based on the above data answer the given subquestions.

Find E[Y ]. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.66 (accepted within ±0.02)

Question 15 on its own page

Question 16

+3 marksOne correct option

Based on the above data answer the given subquestions.

Find the probability density function of Y .

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

Correct answer

  • B
Question 16 on its own page