Suppose you work for a news agency, which is conducting an exit poll for the MCD (Municipal Corporation of Delhi) elections. You have been tasked with predicting the winner for ward 75N (Ashok Vihar). You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.0.58; 0.2460.58; 0.4960.58; 0.494None of the above
Question
Suppose you work for a news agency, which is conducting an exit poll for the MCD (Municipal Corporation of Delhi) elections. You have been tasked with predicting the winner for ward 75N (Ashok Vihar). You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.0.58; 0.2460.58; 0.4960.58; 0.494None of the above
Solution
The question is asking for the mean and standard deviation of the proportion of people that voted for AAP (X).
Step 1: Calculate the mean The mean (μ) is calculated as the sum of all values divided by the number of values. In this case, the mean would be the proportion of people that voted for AAP, which is 58 out of 100, or 0.58.
Step 2: Calculate the standard deviation The standard deviation (σ) is a measure of how spread out the numbers in a data set are around the mean. In this case, it would be calculated using the formula for the standard deviation of a binomial distribution, which is sqrt[np(1-p)], where n is the number of trials (100 voters), p is the probability of success (voting for AAP, or 0.58), and 1-p is the probability of failure (not voting for AAP, or 0.42).
So, σ = sqrt[1000.58(1-0.58)] = sqrt[1000.580.42] = sqrt[24.36] = 0.494
Therefore, the mean and standard deviation of X are 0.58 and 0.494, respectively. So, the correct answer is "0.58; 0.494".
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