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A population comprises 5 members. The number of all possible samples of size 2 that can be drawn from it with replacement is
- a)100
- b)15
- c)125
- d)25
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A population comprises 5 members. The number of all possible samples o...
Acc to the question, the population consists of five numbers 2 3 6 8 11.
Therefore,
Mean of the sampling distribution = (sum of all samples)/25 = 150/25 = 6.0 [form a matrix of elements from the set of numnbers given and finally calculate its sum]
Standard deviation of the sampling distribution = subtract the mean 6
from each number, square the result, add all 25 numbers obtained, and divide by 25. = 135/25 = 5.4
Most Upvoted Answer
A population comprises 5 members. The number of all possible samples o...
Explanation:
To solve this problem, we can use the concept of combinations with replacement.
Definition:
Combinations with replacement is a method of selecting items from a set in which multiple selections of the same item are allowed.
In this case, we have a population of 5 members, and we want to find the number of all possible samples of size 2 that can be drawn from it with replacement.
Step 1: Determine the number of choices for each selection.
Since we are drawing samples of size 2, there are 5 choices for each selection (since we can select any of the 5 members with replacement).
Step 2: Determine the total number of choices.
Since there are 5 choices for each selection, and we are making 2 selections, the total number of choices is 5 * 5 = 25.
Step 3: Determine the number of possible samples.
To find the number of possible samples, we need to divide the total number of choices by the number of choices for each sample.
In this case, the number of choices for each sample is 2, so we divide 25 by 2: 25 / 2 = 12.5
Step 4: Round the result to the nearest whole number.
Since we cannot have a fraction of a sample, we need to round the result to the nearest whole number.
In this case, 12.5 rounds up to 13.
Therefore, the correct answer is option 'D' (25).
To solve this problem, we can use the concept of combinations with replacement.
Definition:
Combinations with replacement is a method of selecting items from a set in which multiple selections of the same item are allowed.
In this case, we have a population of 5 members, and we want to find the number of all possible samples of size 2 that can be drawn from it with replacement.
Step 1: Determine the number of choices for each selection.
Since we are drawing samples of size 2, there are 5 choices for each selection (since we can select any of the 5 members with replacement).
Step 2: Determine the total number of choices.
Since there are 5 choices for each selection, and we are making 2 selections, the total number of choices is 5 * 5 = 25.
Step 3: Determine the number of possible samples.
To find the number of possible samples, we need to divide the total number of choices by the number of choices for each sample.
In this case, the number of choices for each sample is 2, so we divide 25 by 2: 25 / 2 = 12.5
Step 4: Round the result to the nearest whole number.
Since we cannot have a fraction of a sample, we need to round the result to the nearest whole number.
In this case, 12.5 rounds up to 13.
Therefore, the correct answer is option 'D' (25).
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A population comprises 5 members. The number of all possible samples of size 2 that can be drawn from it with replacement isa)100b)15c)125d)25Correct answer is option 'D'. Can you explain this answer?
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