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In a binomial distribution n=20, q=0.75....

In a binomial distribution `n=20, q=0.75`. Then mean =

A

5

B

15

C

10

D

7.5

Text Solution

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The correct Answer is:
To find the mean of a binomial distribution given \( n = 20 \) and \( q = 0.75 \), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the values of \( n \) and \( q \)**: - We are given \( n = 20 \) and \( q = 0.75 \). 2. **Calculate \( p \)**: - The probability of success \( p \) is calculated using the formula: \[ p = 1 - q \] - Substituting the value of \( q \): \[ p = 1 - 0.75 = 0.25 \] 3. **Use the formula for the mean of a binomial distribution**: - The mean \( \mu \) of a binomial distribution is given by: \[ \mu = n \cdot p \] - Substituting the values of \( n \) and \( p \): \[ \mu = 20 \cdot 0.25 \] 4. **Calculate the mean**: - Performing the multiplication: \[ \mu = 20 \cdot 0.25 = 5 \] 5. **Conclusion**: - Therefore, the mean of the binomial distribution is: \[ \mu = 5 \]
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