Match List – I with List – II.
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LIST I |
LIST II |
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A. In a binomial distribution, if n = 10, p = 0.25, then its mean is: |
I. 5 |
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B. In a binomial distribution, if n = 20, p = 0.5, then its variance is: |
II. 25 |
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C. In a binomial distribution, if mean is 5 and variance is 4 then the number of trials is: |
III. 2 |
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D. A coin is tossed 8 times. Then the variance of number of tails obtained is, |
IV. 2.5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-I, C-II, D-III
$\text{A: Mean} = np = 10 \cdot 0.25 = 2.5 \Rightarrow \text{IV}$
$\text{B: Variance} = npq = 20 \cdot 0.5 \cdot 0.5 = 5 \Rightarrow \text{I}$
$\text{C: Mean} = np = 5,\ \text{Variance} = npq = 4$
$npq = 4 \Rightarrow 5q = 4 \Rightarrow q = \frac{4}{5},\ p=\frac{1}{5}$
$n \cdot \frac{1}{5} = 5 \Rightarrow n = 25 \Rightarrow \text{II}$
$\text{D: Variance} = npq = 8 \cdot \frac{1}{2} \cdot \frac{1}{2} = 2 \Rightarrow \text{III}$
$\text{A-IV,\ B-I,\ C-II,\ D-III}$