The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 13 Apr 2025, in the January 2025 term, set QDD1: 18 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.
A box contains 10 marbles, 6 of which are red and 4 are blue. A sample of 4 marbles is randomly selected without replacement. Let the random variable X represent the number of red marbles in the selected sample. Identify the distribution of X.
Hypergeometric
Poisson
Binomial
Uniform
Correct answer
Hypergeometric
64
18
16
32
Correct answer
64
318240
78000
18720
39000
Correct answer
78000
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. Find the number of possible arrangements such that D and E cannot sit next to each other.
3600
4320
5040
720
Correct answer
3600
Which of the following option(s) is/are correct for a variable with an ordinal scale of measurement?
The data can be arranged in a meaningful order.
Arithmetic operations like addition and subtraction are valid.
The intervals between values are equal and meaningful.
The mode and median can be determined, but not the mean.
Correct answers
The data can be arranged in a meaningful order.
The mode and median can be determined, but not the mean.
Correct answer: 3.67 (accepted within ±0.03)
Correct answer: 0.54 (accepted within ±0.03)
A call center receives customer calls and the number of calls received per hour follows a Poisson distribution with a mean rate of 6 calls per hour. What is the probability that at most 2 calls are received in 30 minutes? Enter the answer correct to two decimal places.
Correct answer: 0.42 (accepted within ±0.03)
Consider a dataset such as 8, 12, 16, 24, and 20. Suppose we multiply all observations by 3. Based on the given information answer the sub questions.
What will be the 25th percentile of the new dataset?
Correct answer: 36
Consider a dataset such as 8, 12, 16, 24, and 20. Suppose we multiply all observations by 3. Based on the given information answer the sub questions.
Find IQR of the new dataset.
Correct answer: 24
Based on the above data, answer the given subquestions.
Correct answer
Based on the above data, answer the given subquestions.
0.023
0.230
0.346
0.035
Correct answer
0.346
Based on the above data, answer the given subquestions.
If the probability that the vendor sells exactly 2 items in a day is 0.30, then find the value of a. Enter the answer correct to two decimal places.
Correct answer: 0.45 (accepted within ±0.02)
Based on the above data, answer the given subquestions.
What is the probability that the vendor sells at least 2 items in a day? Enter the answer correct to two decimal places.
Correct answer: 0.55 (accepted within ±0.02)
Based on the above data, answer the given subquestions.
Correct answer: 34
Based on the above data, answer the given subquestions.
—
Correct answer
The time taken by a coffee machine to brew a cup of coffee is uniformly distributed between 2 and b minutes. Based on this information, answer the given subquestions:
If the expected time for the coffee machine to brew a cup of coffee is 8.5 minutes, then find the value of b.
Correct answer: 15
The time taken by a coffee machine to brew a cup of coffee is uniformly distributed between 2 and b minutes. Based on this information, answer the given subquestions:
If the coffee machine has been brewing for more than 6 minutes, what is the probability that it will finish brewing between 6 and 10 minutes?
Correct answer
