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If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61?
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If a binomial distribution is fitted to the following data: then the X...
Solution:
Given,
X: 0, 1, 2, 3, 4
f: 16, 25, 32, 17, 10
We need to fit a binomial distribution and find the sum of expected frequencies for x = 2, 3, and 4.
Steps to fit a binomial distribution:
1. Find the value of n, the number of trials.
n = ∑f = 16 + 25 + 32 + 17 + 10 = 100
2. Find the value of p, the probability of success in each trial.
p = x/n = (0*16 + 1*25 + 2*32 + 3*17 + 4*10)/100 = 0.97
3. Use the binomial distribution formula to find the expected frequency for each value of x.
E(x) = nCxf^x(1-f)^(n-x)
Expected frequencies for x = 2, 3, and 4:
E(2) = 100C2 * 0.97^2 * (1-0.97)^(100-2) ≈ 29.7
E(3) = 100C3 * 0.97^3 * (1-0.97)^(100-3) ≈ 28.9
E(4) = 100C4 * 0.97^4 * (1-0.97)^(100-4) ≈ 13.1
4. Sum up the expected frequencies for x = 2, 3, and 4.
Sum of expected frequencies = E(2) + E(3) + E(4) ≈ 29.7 + 28.9 + 13.1 ≈ 71.7
Therefore, the sum of expected frequencies for x = 2, 3, and 4 is approximately 71.7, which is closest to option (c) 60.
Given,
X: 0, 1, 2, 3, 4
f: 16, 25, 32, 17, 10
We need to fit a binomial distribution and find the sum of expected frequencies for x = 2, 3, and 4.
Steps to fit a binomial distribution:
1. Find the value of n, the number of trials.
n = ∑f = 16 + 25 + 32 + 17 + 10 = 100
2. Find the value of p, the probability of success in each trial.
p = x/n = (0*16 + 1*25 + 2*32 + 3*17 + 4*10)/100 = 0.97
3. Use the binomial distribution formula to find the expected frequency for each value of x.
E(x) = nCxf^x(1-f)^(n-x)
Expected frequencies for x = 2, 3, and 4:
E(2) = 100C2 * 0.97^2 * (1-0.97)^(100-2) ≈ 29.7
E(3) = 100C3 * 0.97^3 * (1-0.97)^(100-3) ≈ 28.9
E(4) = 100C4 * 0.97^4 * (1-0.97)^(100-4) ≈ 13.1
4. Sum up the expected frequencies for x = 2, 3, and 4.
Sum of expected frequencies = E(2) + E(3) + E(4) ≈ 29.7 + 28.9 + 13.1 ≈ 71.7
Therefore, the sum of expected frequencies for x = 2, 3, and 4 is approximately 71.7, which is closest to option (c) 60.
Community Answer
If a binomial distribution is fitted to the following data: then the X...
61
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If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61?
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If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61?.
If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a binomial distribution is fitted to the following data: then the X : 0. 1. 2. 3. 4 f : 16 25 32 17 10 then the sum of the expected frequencies for x 2, 3 and 4 would be (a) 58 (b) 59 (c) 60 (d) 61?.
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