Question

If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of at least 7 successes is

• A. \( \frac{3}{214} \)
• B. \( \frac{4}{173} \)
• C. \( \frac{9}{256} \)
• D. \( \frac{7}{231} \)

Hint:

For binomial distributions, the mean \( \mu = n \cdot p \) and variance \( \sigma^2 = n \cdot p \cdot (1 - p) \). Use these formulas to calculate \( n \) and \( p \), then apply the binomial probability formula.

Answer 1

The Correct Option is C

The probability for a binomial distribution can be calculated using the formula for binomial probability. Given that the mean \( \mu = 4 \) and variance \( \sigma^2 = 2 \), we calculate the values for \( n \) and \( p \). Then we apply these values to find the probability of getting at least 7 successes.