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Mathematics-IV Unit 4 – Statistical Techniques II: important questions for AKTU

Unit 4 (Statistical Techniques II) questions that AKTU repeats most often. This unit carries about 30 marks per paper. Start with the repeated questions, then the most asked topics.

Most repeated Unit 4 questions

  • A sample of 100 dry battery cells tested to find the length of life produced the following results: 𝑥̅ = 12 hours, σ = 3 hours. Assuming the data to be normally distributed, what percentage of battery cells are expected to have life (i) more than 15 hours (ii) less than 6 hours (iii) between 10 and 14 hours. (10 marks, 2021, Normal Distribution) – also asked in 2022, 2023, 2024, 2025, 2026
  • In a test on 2000 electric bulbs, the life was normally distributed with average life of 2040 hours and S.D of 60 hours. Calculate the number of bulbs likely to burn for: (i) More than 2150 hours, (ii) less than 1950 hours, (iii) between 1920 hours and 2160 hours. (10 marks, 2022, Normal Distribution) – also asked in 2023, 2024, 2025, 2026
  • The income of a group of 10,000 persons was found to be normally distributed with mean 750 Rs. per month and S.D. of 50 Rs. Show that about 95% had income exceeding 668 Rs and only 5% had income exceeding 832 Rs. Also determine the lowest income among the richest 100. (7 marks, 2024, Normal Distribution) – also asked in 2021, 2022, 2025

Most important Unit 4 topic

  • Probability and Random Variables (Unit 4: Statistical Techniques II) – asked 20 times in 2021, 2022, 2023, 2024, 2025, 2026

Most asked Unit 4 topics

  • Probability and Random Variables – asked 20 times
  • Normal Distribution – asked 11 times
  • Binomial Distribution – asked 10 times

More Unit 4 previous year questions

  • Define a probability density function (p.d.f.) and state its two properties. (2 marks, 2026, Probability and Random Variables)
  • The lifetime of an electric bulb is normally distributed with mean 1200 hours and standard deviation 100 hours. 1. Find the probability that a bulb lasts (a) more than 1300 hours, (b) between 1100 and 1250 hours. 2. Out of 2000 bulbs, how many are expected to last more than 1400 hours? (7 marks, 2026, Normal Distribution)
  • The number of typing errors per page in a book follows a Poisson distribution with mean 2. 1. Find the probability that a randomly chosen page has (a) no error (b) at most two errors. 2. If a book has 500 pages, estimate the expected number of pages with exactly three errors. (7 marks, 2026, Poisson Distribution)
  • A discrete random variable X has the following probability distribution: x: 0 1 2 3 4, P(X=x): k 2k 3k 2k k. Find the value of k and determine the mean and variance of X. (7 marks, 2026, Probability and Random Variables)
  • Find p and q of Binomial distribution whose mean is 9 and variance 9/4. (2 marks, 2025, Binomial Distribution)

Unit 4 syllabus topics

  • Probability and Random Variables
  • Binomial Distribution
  • Poisson Distribution
  • Normal Distribution