For budgeting purposes, each manager in a company must estimate their group’s monthly expenses. Manager 1 estimates that his monthly expenses are normally distributed with mean $21,000 and standard deviation $3,000. Manager 2 estimates that her monthly expenses follow a discrete distribution with p($15,000) = 0.2, p($20,000) = 0.4, p($25,000) = 0.3, and p($30,000) = 0.1.

a: For each manager, compute the mean and standard deviation of their group’s monthly expenses.

b: For each manager, estimate the probabilities that their group’s monthly expenses are:
i) between $17,000 and $24,000, ii) higher than $22,000, iii) below $18,000, and iv) exactly $25,000.

c: The company wants to budget enough for each group so that the probability of expenses being over budget is at most 15%. How much should the company budget for
each manager?