Question

3. After shipping bags of parts, it was learned that an intern dumped a box of defective pieces into the hopper that is continuously mixed. There were 250 bad pieces put into the hopper that held 1800 pieces (including the bad ones). There were 1200 pieces still in the hopper when it was discovered. If each package contained 8 pieces, how many can be expected to contain a defective piece? (20 points)

Answer 1

There were 250 bad pieces in 1800 pieces.

Probability of a defective hopper, p = 250 / 1800 = 0.1389

There were 1200 pieces still remaining. So, 1800 - 1200 = 600 pieces were placed in packages.

Each package contains 8 pieces.

So, number of packages, n = 600 / 8 = 75

Probability that there are no defective piece in 8 pieces = (1 - 0.1389)⁸ = 0.3023

Probability that a package contain a defective piece = 1 - 0.3023 = 0.6977

Expected number of packages to contain a defective piece = number of packages * Probability that a package contain a defective piece

= 75 * 0.6977

= 52.3275