Question

The weight of a bag of potato chips is stated as 300 g. The amount that the packaging machine puts in each bag is normally distributed with mean 306 g and standard deviation 3.6 g. (a) (4 points) What is the proportion of all bags sold that are underweight? (b) (3 points) A ”bargain pack” contains two bags. Find the probability that both are underweight. (c) (5 points) Find the probability that the average weight of the bags in a bargain pack is below 300 g.

Answer 1

Mean, = 306 g

Standard deviation, = 3.6 g

Let X denote the weight of a randomly selected bag of potato chips

(a) The proportion of all bags sold that are underweight

= P(X < 300)

= P{Z < (300 - 306)/3.6}

= P(Z < -1.667)

= 0.0478 = 4.78%

(b) The probability that both the bag are underweight

= = 0.0023

(c) The sampling distribution of the average weight of the bags in a bargain pack has Mean = 306 g

and standard deviation = 3.6/√2 = 2.546

The probability that the average weight of the bags in a bargain pack is below 300 g = P( < 300)

= P{Z < (300 - 306)/2.546}

= P(Z < -2.357)

= 0.0092