Question

In a certain town, 23% of males have a beard. In random samples of 10 men from

this town, what are the mean and standard deviation of the number of men with
a beard?

Answer 1

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.