25% of the students in an English class of 100 are international students. Find mean, and standard deviation of this binomial distribution
To find the mean and standard deviation of a binomial distribution, we need to know the probability of success and the number of trials.
In this case, the probability of success is 25% or 0.25, and the number of trials is 100 (since there are 100 students in the English class).
The mean (μ) of a binomial distribution is calculated using the formula:
μ = n * p
where n is the number of trials and p is the probability of success.
Substituting the given values:
μ = 100 * 0.25
μ = 25
So, the mean of this binomial distribution is 25.
The standard deviation (σ) of a binomial distribution is given by the formula:
σ = sqrt(n * p * (1 - p))
Substituting the given values:
σ = sqrt(100 * 0.25 * (1 - 0.25))
σ = sqrt(100 * 0.25 * 0.75)
σ = sqrt(18.75)
σ ≈ 4.33
So, the standard deviation of this binomial distribution is approximately 4.33.