The weight of potato chips in a medium-size bag is stated to be 8 ounces. The am

Question

The weight of potato chips in a medium-size bag is stated to be 8 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 8.1 ounces and a standard deviation of 0.07 ounces. What fraction of all bags sold are underweight? Some of the chips are sold in "bargain packs" of 3 bags. What's the probability that none of the 3 is underweight? What's the probability that the mean weight of the 3 bags is below the stated amount? What's the probability that the mean weight of a 20-bag case of potato chips is below 8 ounces? The fraction of all bags sold that are underweight is. (Round to four decimal places as needed.)

Explanation / Answer

Mean =8.1 and std dev = 0.07

a) Underweight = wt < 8

i.e. z<-0.1/0.07 =- 1.423

Prob (Z<-0.1423) = 0.5-0.4222

=0.0778

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c) for sample size 3, std dev = 0.07/rt 3= 0.0404

Hence P(x<8) = P(Z<-0.1/0.0404) = P(Z<-2.47)

=0.068

b) Prob that none is underweight = (1-0.068)^3

= 0.8096

c) For n =20 st dev = 0.07/rt 20 = 0.0157

X<8 means Z<-0.1/0.0157

P(Z<-6.388) = 1

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