Question

The mean and variance, respectively, of a binomial distribution for \( n \) independent trials with the probability of success as \( p \), are

• A. \( \sqrt{np} \), \( np(1 - 2p) \)
• B. \( \sqrt{np} \), \( \sqrt{np(1 - p)} \)
• C. \( np \), \( np \)
• D. \( np \), \( np(1 - p) \)

Hint:

For a binomial distribution with parameters \( n \) and \( p \), the mean is \( np \) and the variance is \( np(1 - p) \).

Answer 1

The Correct Option is D

For a binomial distribution with parameters \( n \) and \( p \) (number of trials and probability of success), the mean and variance are given by the following formulas:

- The mean \( \mu \) is: \[ \mu = np \] - The variance \( \sigma^2 \) is: \[ \sigma^2 = np(1 - p) \] Thus, the mean is \( np \) and the variance is \( np(1 - p) \), which corresponds to option (D).
Final Answer: (D)