Final answer:
The mean number of males selected each month is 3.2, and the standard deviation is approximately 1.4 males.
Step-by-step explanation:
The student's question is about finding the mean and standard deviation of the number of males selected each month to have lunch with the CEO in a division of a company. Given that 40% of the employees are male, we can determine the mean number of males selected for the lunch by multiplying the percentage of males by the number of employees selected each month, this is known as the expected value, E(X) = np. Since 40% of over 200 employees are male, we assume we have at least 80 males (0.40 x 200) in the division. If 8 employees are selected at random, the mean number of males expected, μ, would be 40% of 8, or 3.2 males.
To find the standard deviation, σ, we use the formula for the standard deviation of a binomial distribution, which is σ = sqrt(np(1-p)), where p is the probability of choosing a male (0.40) and n is the total number selected (8). In this case, the standard deviation is σ = sqrt((8)(0.40)(0.60)) and rounding to the nearest tenth gives us σ ≈ 1.4.