Final answer:
The mean and standard deviation of the number of students with 20/20 vision in the class can be found using the binomial distribution. The mean is 4.4 and the standard deviation is 1.98.
Step-by-step explanation:
To find the mean and standard deviation of the number of students with 20/20 vision in the class, we can use the binomial distribution. Let's define X as the number of students with 20/20 vision. The mean of X is given by the formula μ = n * p, where n is the total number of trials (40 students) and p is the probability of success (0.11). So, the mean is μ = 40 * 0.11 = 4.4.
The standard deviation of X is given by the formula σ = √(n * p * (1 - p)). So, the standard deviation is σ = √(40 * 0.11 * (1 - 0.11)) = √(4.4 * 0.89) = √3.916 = 1.98 (rounded to two decimal places).