A company of N = 10,000 employees initiates an employee productivity study in which the productivity of each employee is rated on a scale from 1 to 5. Suppose that 200 of the employees are rated 1, 400 are rated 2, 3000 are rated 3, 3400 are rated 4, and the rest are rated 5. A pilot study into the degree of employee satisfaction at work interviews 10 randomly selected employees of this company. The productivity ratings of the 10 selected employees are x1 =1, x2 =x3 =x4 =2, x5 =x6 =3, x7 =x8 =x9 =4, x10 =5.

a)Compute the population mean, and the population standard deviation, of the productivity ratings of all employees in the company. Please denote your answers using the correct mathematical notations.

b)Compute the sample mean, and the sample standard deviation, of the productivity ratings of the 10 selected employees. Please denote your answers using the correct mathematical notations.