The weight of potato chips in a mediumsize bag is stated to

The weight of potato chips in a medium-size bag is stated to be 12 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 12.1 ounces and a standard deviation of 0.07ounces.

a) What fraction of all bags sold are underweight?

b) Some of the chips are sold in \"bargain packs\" of 3 bags. What\'s the probability that none of the 3 is underweight?

c) What\'s the probability that the mean weight of the 3 bags is below the stated amount?

d) What\'s the probability that the mean weight of a 24-bag case of potato chips is below 12 ounces?

Solution

(a)Fraction of bags underweight=0.0765637

(b)Probability of none of the 3bags underweight=(1-0.0765637)³=0.787446

(c)Probability that mean weight of the 3 bags is below the stated amount=0.0066738

(d)Probability that mean weight of the 24-bag case is below the stated amount=0