We can approach this problem as a binomial distribution with n = 10 trials (sampling 10 men) and p = 0.23 probability of success (a man having a beard).
The mean of the binomial distribution is given by:
μ = n * p
μ = 10 * 0.23
μ = 2.3
So, the mean number of men with a beard in a random sample of 10 men is 2.3.
The standard deviation of the binomial distribution is given by:
σ = sqrt(n * p * (1 - p))
σ = sqrt(10 * 0.23 * (1 - 0.23))
σ = 1.33 (rounded to two decimal places)
So, the standard deviation of the number of men with a beard in a random sample of 10 men is 1.33.
Therefore, the mean and standard deviation of the number of men with a beard in a random sample of 10 men from the town are 2.3 and 1.33, respectively.