Question

If the mean number of successes in a binomial distribution is 5 and the probability of success is 0.4, what is the number of trials?

• A. 10
• B. 8
• C. 6.25
• D. 12.5

Answer 1

Answer: (D)

12.5

Answer 2

To find the number of trials in a binomial distribution, we use the formula for the mean of a binomial distribution.

Given:

• Mean number of successes ($\mu$) = 5
• Probability of success (p) = 0.4

Formula for the mean of a binomial distribution:

The mean ($\mu$) of a binomial distribution is given by the product of the number of trials (n) and the probability of success (p): $\mu = np$

Substitute the given values into the formula:

$5 = n \times 0.4$

Solve for n (number of trials):

$n = \frac{5}{0.4}$

$n = \frac{5}{\frac{4}{10}}$

$n = \frac{5 \times 10}{4}$

$n = \frac{50}{4}$

$n = 12.5$

Thus, the number of trials is 12.5.