Number of products with errors within a day is distributed as:
......x............ 0........... 1........... 2......... 3 ............4
P(X = x)..... 0.8........ 0.1....... 0.05.... 0.03........ 0.02
where X is the number of faulty products in a day. We assume that the number of faulty products in different days is independent of each other.
a) Find E(X) and Var(X). What is the probability of no defective product, the probability of at least one faulty product and find probability of at least three defective products.
b) Calculate the probability that there will be at least one faulty product within a working week of five days.
Calculate the probability that there is exactly a product with errors during a working week of five days.
The cost per. day as a function of the number of faulty products, x, follows the formula 150x^2
c) What is the expected cost resulting from faulty products within one year (252 days of production)? What is the standard deviation?