Question

Bags of potato chips have a mean weight of 6 ounces with a standard deviation of 0.2 ounces. There are 100 bags of potato chips in a box.

(i) What is the probability that the total weight of the 100 bags is greater than 603 ounces?

(ii) A potato chip factory produces 1000 boxes of potato chips. What is the probability that more than 70 of these boxes contain more than 603 ounces of potato chips?

Answer 1

Please note: Z = (X - )/[/sqrt(n)]. Therefore when multiplying by a constant c, the new Mean = c * Old mean. Whereas the new standard deviation (new) = old * sqrt(c)

(i) n = 100 bags, = 6 ounces/bag, = 0.2/bag

Probability that the total weight of 100 bags is greater than 603 ounces.

Average weight of 100 bags (1 box) = 6 * 100 = 600

Standard deviation of 100 bags (1 box) = 0.2 * Sqrt(100) = 0.2 * 10 = 2

Therefore P(X > 603) = 1 - P(X < 603)

For P(X < 603); Z = (603 - 600)/2 = 1.5   (n = 1, as we are doing it for 1 box selected at random containing 100 bags)

The probability P(X < 603) = 0.9332

Therefore P(X > 603) = 1 - 0.9332 = 0.0668

_____________________________________________________________________________

n = 70 boxes, = 600 ounces/box, = 2 ounces/box

Therefore P(X > 603) = 1 - P(X < 603)

For P(X < 603); Z = (603 - 600)/[2/sqrt(70)] = 12.55

The probability P(X < 603) = 1

Therefore P(X > 603) = 1 - 1 = 0.00