If 80% of the applicants are able to pass a driver's proficiency road test, find the mean, variance, and standard deviation of the number of people who pass the test in a sample of 300 applicants.

To find the mean, variance, and standard deviation, we can use the binomial distribution formula. In this case, the probability of passing the test is 80% or 0.8, and the sample size is 300.

1. Mean (μ):
The mean is calculated using the formula: μ = n * p, where n is the sample size and p is the probability of success. In this case, μ = 300 * 0.8 = 240.

2. Variance (σ^2):
The variance is calculated using the formula: σ^2 = n * p * (1 - p), where n is the sample size and p is the probability of success. In this case, σ^2 = 300 * 0.8 * (1 - 0.8) = 48.

3. Standard deviation (σ):
The standard deviation is calculated by taking the square root of the variance: σ = sqrt(σ^2). In this case, σ = sqrt(48) = 6.93 (rounded to two decimal places).

So, the mean number of people who pass the test is 240, the variance is 48, and the standard deviation is 6.93.