Mathematics-IV Unit 4 Notes AKTU (BAS303)

AKTU · BTECH · Semester 3, 4 · Mathematics-IV · Unit 4 · Notes

AKTU Mathematics-IV (BAS303) Unit 4 notes for B.Tech Semester 3/4 – Statistical Techniques II. Topics: Probability and Random Variables, Binomial…

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Unit 4: Statistical Techniques II – AKTU syllabus topics

  • Probability and Random Variables: PMF and PDF, Expectation and Variance
  • Binomial Distribution
  • Poisson Distribution
  • Normal Distribution

Most asked AKTU PYQ questions from Unit 4

  1. Q6b. 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… (10 marks, 2020-21)
  2. Q2d. 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, 2021-22)
  3. Q6b. If X follows Poisson distribution such that P(X=2) = 9P(X=4) + 90P(X=6), find mean, variance and distribution. (10 marks, 2022-23)
  4. Q6b. 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, 2023-24)
  5. Q2d. In a sample of 1000 cases, the mean of a certain test is 14 and S.D is 2.5. Assuming the distribution to be normal, find: (i) How many students score between 12 and 15? (ii) How many score above 18? (iii) How many score below 8? Given f(0.8)=0.2881, f(0.4)=0.1554, f(1.6)=0.4452, f(2.4)=0.4918. (10 marks, 2021-22)
  6. Q2d. 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, 2025-26)
  7. Q2d. If the heights of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches, find the height below which 99% of the students lie (P(z=2.327)=0.49). (7 marks, 2024-25)
  8. Q6b. In a sample of 1000 cases, the mean of a certain test is 14 and S.D. is 2.5. Assuming the distribution to be normal, find (i) How many students score between 12 and 15? (ii) How many score above 18? (iii) How many score below 8? (iv) How many score 16? Given P(Z=0.8)=0.2881, P(Z=0.4)=0.1554,… (7 marks, 2024-25)
  9. Q2d. If Z is a standard normal variable, find the following probabilities: (i) P(Z < 1.2) (ii) P(Z > -1.2) (iii) P(-1.2 < Z < 1.3). (7 marks, 2024-25)
  10. Q6b. The daily wages of 1000 workers are distributed around a mean of Rs.140 and with a standard deviation of Rs.10. Estimate the number of workers whose daily wages will be (i) between Rs.140 and Rs.144 (ii) less than Rs.126 (iii) more than Rs.160. (7 marks, 2023-24)

AKTU paper codes: BAS303, BAS303H, BAS403, BAS403H, KAS302, KAS402

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