Question

The weight of potato chips in a largelarge​-size bag is stated to be 16 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 16.3 ounces and a standard deviation of 0.17ounces. ​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 30​-bag case of potato chips is below 16 ​ounces?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	16.3
std deviation   =σ=	0.170

a)

probability =P(X<16)=(Z<(16-16.3)/0.17)=P(Z<-1.76)=0.0392

b)

probability that none of the 3 is​ underweight =(1-0.0392)^3=0.8869

c)

sample size       =n=	3
std error=σx̅=σ/√n=	0.09815

probability =P(Xbar<16)=(Z<(16-16.3)/0.098)=P(Z<-3.06)=0.0011

d)

sample size       =n=	30
std error=σx̅=σ/√n=	0.03104

probability =P(X<16)=(Z<(16-16.3)/0.031)=P(Z<-9.67)=0.000