The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of trials, where each trial has the same probability of success.

In a binomial distribution, there are two parameters:
- n: the number of trials
- p: the probability of success in each trial

The mean of a binomial distribution is given by the product of the number of trials and the probability of success:
Mean (μ) = n * p

The standard deviation of a binomial distribution is given by the square root of the product of the number of trials, the probability of success, and the probability of failure:
Standard Deviation (σ) = √(n * p * q)

Where q = 1 - p (probability of failure)


Mean (μ) = 20
Standard Deviation (σ) = 4


We are given the mean (μ) and standard deviation (σ) of the binomial distribution.

From the formula for the mean, we can write:
20 = n * p

From the formula for the standard deviation, we can write:
4 = √(n * p * q)

Squaring both sides of the equation for the standard deviation, we get:
16 = n * p * q

Using the value of p from the equation for the mean, we can substitute it into the equation for the standard deviation:
16 = n * (20/n) * (1 - 20/n)

Simplifying the equation, we get:
16 = 20 - 20^2/n + 20

Simplifying further, we get:
16 = 40 - 400/n

Rearranging the equation, we get:
400/n = 40 - 16
400/n = 24

Cross multiplying, we get:
24n = 400

Dividing both sides by 24, we get:
n = 400/24 = 16.67

Since n represents the number of trials, it must be a whole number. Therefore, the closest whole number to 16.67 is 17.

Thus, the correct answer is option 'B' - 100.