Question

Let X be the random variable giving the number of sick days taken by the “typical” worker per year. Suppose that it is known that E(X) = μ = 10, and that the standard deviation of X is σ = 2. (both μ and σ are measured in days. A firm has n = 64 employees. Consider these to be a random sample from the population of all “typical” employees.

a) What is the approximate distribution of the average number of sick days taken by this firm’s employees?

b) What is the probability that the average number of sick days taken by the firm’s employees lies between 9.8 days and 10.2 days?

c) The CFO (Chief Financial Officer) of the firm is preparing next year’s budget. How many sick days should the CFO put into the budget if the CFO wants the probability of exceeding the number of days budgeted to be less than 10%?

Hint: If ?? = number of sick days taken by employee j (1≤ j ≤ 64) , then ?? ̅̅̅̅ = ∑ ?? ? 1 ? is the sample mean, and ∑ ?? ? 1 = total number of sick days taken

Answer 1