Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
BSMA1002 · Statistics for Data Science I
Binomial, Poisson & hypergeometric
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
End Term · 31 Aug 2025 (FN)End Term
Read the passage below, then answer Q1–Q2
Based on the above data, answer the given subquestions.
Q1MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q2NAT2 Marks·Write the number
Your answer:
End Term · 31 Aug 2025 (AN)End Term
- Q3NAT3 Marks·Write the number
The number of vehicles passing through a highway toll booth in a minute follows a Poisson distribution with mean λ = 4. Find the probability that at most two vehicle pass through highway toll booth in a minute. Enter the answer correct to two decimal places. (Use : e^4 = 54.60, e^(1/4) = 1.28, e^(-4) = 0.02, e^(-1/4) = 0.78)
Your answer:
End Term · 13 Apr 2025 (FN)End Term
- Q4MCQ1 Mark·Choose one option
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.
- AHypergeometric
- BPoisson
- CBinomial
- DUniform
- Q5NAT3 Marks·Write the number
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.
Your answer: Read the passage below, then answer Q6–Q7
Based on the above data, answer the given subquestions.
Q6MCQ2 Marks·Choose one option
- A
- B
- C
- D
- A
- Q7MCQ2 Marks·Choose one option
- A0.023
- B0.230
- C0.346
- D0.035
End Term · 13 Apr 2025 (AN)End Term
- Q8MCQ2 Marks·Choose one option
- A21.5
- B20
- C5.38
- D5
Read the passage below, then answer Q9–Q10
A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.
Q9MCQ3 Marks·Choose one optionFind probability that the wheel lands on red exactly 2 times out of the three spins.
- A
- B
- C
- D
- A
- Q10NAT2 Marks·Write the number
Find the value of E(X). Enter the answer correct to two decimal places.
Your answer:
End Term · 22 Dec 2024 (FN)End Term
- Q11MCQ3 Marks·Choose one option
If the Indian cricket team has a 60% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
- A0.26
- B0.078
- C0.34
- D0.68
- Q12MCQ3 Marks·Choose one option
- A{0,1,2,3,4}
- B{0,1,2,3}
- C{0,1,2}
- D{0,1,2,3,4,5}
- Q13MCQ4 Marks·Choose one option
The number of customers entering in a store follows a Poisson distribution with an average rate of 12 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
- A
- B
- C
- D
- A
End Term · 22 Dec 2024 (AN)End Term
- Q14MCQ3 Marks·Choose one option
If the Indian cricket team has a 65% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
- A0.31
- B0.12
- C0.43
- D0.57
- Q15MCQ3 Marks·Choose one option
- A{0,1,2,3,4}
- B{0,1,2,3}
- C{0,1,2}
- D{0,1,2,3,4,5}
- Q16MCQ4 Marks·Choose one option
The number of customers entering in a store follows a Poisson distribution with an average rate of 8 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
- A
- B
- C
- D
- A