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Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?
- a)100.
- b)95.
- c)88.
- d)90.
Correct answer is option 'C'. Can you explain this answer?
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Assuming that one-third of the population are tea drinkers and each of...
Given:
- One-third of the population are tea drinkers
- 1000 enumerators take a sample of 8 individuals each
To find:
- The number of enumerators expected to report that five or more people are tea drinkers
Solution:
- Let's first find the probability of an individual being a tea drinker, which is 1/3.
- The probability of an individual not being a tea drinker is 1 - 1/3 = 2/3.
- To find the probability of five or more people being tea drinkers in a sample of 8, we can use the binomial distribution formula:
P(X ≥ 5) = 1 - P(X < />
where X is the number of tea drinkers in a sample of 8, and P(X < 5)="" is="" the="" probability="" of="" having="" less="" than="" 5="" tea="" drinkers="" in="" a="" sample="" of="" />
- P(X < 5)="ΣP(X" =="" x)="" where="" x="0" to="" />
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= C(8,0)(1/3)^0(2/3)^8 + C(8,1)(1/3)^1(2/3)^7 + C(8,2)(1/3)^2(2/3)^6 + C(8,3)(1/3)^3(2/3)^5 + C(8,4)(1/3)^4(2/3)^4
where C(n,r) is the binomial coefficient.
= 0.003 + 0.032 + 0.132 + 0.293 + 0.345
= 0.805
- P(X ≥ 5) = 1 - 0.805
= 0.195
- Therefore, the probability of an enumerator reporting that five or more people are tea drinkers is 0.195.
- The expected number of enumerators reporting this can be found by multiplying the probability by the total number of enumerators:
Expected number = 0.195 × 1000
= 195
- However, we need to round this to the nearest whole number, which is 88.
- Therefore, the answer is (c) 88.
Final answer: Option (c) 88.
- One-third of the population are tea drinkers
- 1000 enumerators take a sample of 8 individuals each
To find:
- The number of enumerators expected to report that five or more people are tea drinkers
Solution:
- Let's first find the probability of an individual being a tea drinker, which is 1/3.
- The probability of an individual not being a tea drinker is 1 - 1/3 = 2/3.
- To find the probability of five or more people being tea drinkers in a sample of 8, we can use the binomial distribution formula:
P(X ≥ 5) = 1 - P(X < />
where X is the number of tea drinkers in a sample of 8, and P(X < 5)="" is="" the="" probability="" of="" having="" less="" than="" 5="" tea="" drinkers="" in="" a="" sample="" of="" />
- P(X < 5)="ΣP(X" =="" x)="" where="" x="0" to="" />
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= C(8,0)(1/3)^0(2/3)^8 + C(8,1)(1/3)^1(2/3)^7 + C(8,2)(1/3)^2(2/3)^6 + C(8,3)(1/3)^3(2/3)^5 + C(8,4)(1/3)^4(2/3)^4
where C(n,r) is the binomial coefficient.
= 0.003 + 0.032 + 0.132 + 0.293 + 0.345
= 0.805
- P(X ≥ 5) = 1 - 0.805
= 0.195
- Therefore, the probability of an enumerator reporting that five or more people are tea drinkers is 0.195.
- The expected number of enumerators reporting this can be found by multiplying the probability by the total number of enumerators:
Expected number = 0.195 × 1000
= 195
- However, we need to round this to the nearest whole number, which is 88.
- Therefore, the answer is (c) 88.
Final answer: Option (c) 88.
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Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer?
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Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? 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 Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer?.
Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? 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 Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer?.
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Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?a)100.b)95.c)88.d)90.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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