JNTU
JNTU B.Tech II STATISTICAL METHODS FOR DATA SCIENCE Previous Question Paper (March - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
In a certain college, 25% of boys and 10% of girls are studying mathematics. The girls constitute 60% of the student body. (i) What is the probability that mathematics is being studied? (ii) If a student is selected at random and is found to be studying mathematics, find the probability that the student is a girl?
Answer
Let B be the event that a student is a boy and G be the event that a student is a girl. Let M be the event that a student is studying mathematics. Given: P(G) = 0.60, P(B) = 1 - 0.60 = 0.40, P(M|B) = 0.25, and P(M|G) = 0.10.
(i) Using the Law of Total Probability: P(M) = P(M|B)P(B) + P(M|G)P(G) = (0.25)(0.40) + (0.10)(0.60) = 0.10 + 0.06 = 0.16. The probability that a student is studying mathematics is 0.16.
(ii) Using Bayes' Theorem: P(G|M) = (P(M|G)P(G)) / P(M) = (0.10 * 0.60) / 0.16 = 0.06 / 0.16 = 0.375. The probability that the student is a girl given they study mathematics is 0.375.
Assume that the heights of 3000 male students at a college are normally distributed with mean 68 inches and Standard Deviation 3 inches. If 80 samples consisting of 25 students each are obtained. What would be the expected mean and SD of the resulting sampling distribution of the mean if the sampling is done: i) with replacement and ii) without replacement.
Answer
Given: Population mean (μ) = 68 inches, population standard deviation (σ) = 3 inches, population size (N) = 3000, sample size (n) = 25.
For any sampling distribution of the mean, the expected mean is equal to the population mean: E(x̄) = μ = 68 inches.
(i) With replacement: The standard error (SE) is given by σ / √n = 3 / √25 = 3 / 5 = 0.6 inches.
(ii) Without replacement: The standard error includes the finite population correction factor, √((N-n)/(N-1)). SE = (σ / √n) * √((N-n)/(N-1)) = 0.6 * √((3000-25)/(3000-1)) = 0.6 * √(2975/2999) ≈ 0.6 * √0.992 ≈ 0.6 * 0.996 = 0.5976 inches.
Among 100 students 50 are studying Maths, 30 are studying Physics, and 20 are studying Maths and Physics. If a student is chosen at random find the probability that the student is (i) studying Maths or Physics (ii) studying neither Physics nor Maths.
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If X is a continuous random variable with probability density function
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Let X be a random variable with the density function
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If the random variable X takes the values 1, 2, 3 and 4 such that
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Suppose the weights of 500 male students are normally distributed with mean = 150 with a standard deviation of 15. Find the number of students whose weights are between 140 and 165.
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Let X have the density function
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Given that
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It is observed that 174 out of a random sample of 200 truck drivers on highway during night are drunk. Is it valid to state that at least 90% of the truck drivers are drunk? Use 0.05 LOS.
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Two horses A and B were tested according to the time (in seconds) to run a particular track with the following results: Horse A (28, 30, 32, 33, 33, 29, 34), Horse B (29, 30, 30, 24, 27, 29). Test whether two horses have the same running capacity.
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Write the properties of t-distribution.
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In an experiment on immunization of cattle from tuberculosis the following results were obtained:
| Affected | Not affected | |
| Inoculated | 12 | 26 |
| Not Inoculated | 16 | 6 |
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The equation of two Regression lines is
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Show that the maximum value of rank correlation coefficient is 1.
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