Question

The weight of cement in a large​-size bag is stated to be 16 kg. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 16.2kg and a standard deviation of 0.14 kg.

​a) What fraction of all bags sold are​ underweight?

​b) Some of the cement is sold in​ "bargain packs" of 5 bags.​ What's the probability that none of the 5 is​ underweight?

​c) What's the probability that the mean weight of the 5 bags is below the stated​ amount?

​d) What's the probability that the mean weight of a 24​-bag case of cement is below 16 ​kg?

​a) The fraction of all bags sold that are underweight is ----.

​(Round to four decimal places as​ needed.)

​b) The probability that none of the 5 bags is underweight is ----.

​(Round to four decimal places as​ needed.)

​c) The probability that the mean weight of the bargain pack is below the stated amount is -----.

​(Round to four decimal places as​ needed.)

​d) The probability that the mean weight of the case is below 16 ounces is----.

Answer 1

a_)

for normal distribution z score =(X-μ)/σx
mean μ=	16.2
standard deviation σ=	0.14

probability =P(X<16)=(Z<(16-16.2)/0.14)=P(Z<-1.43)=0.0764

b)

probability that none of the 5 is​ underweight =(1-0.0764)^5 =0.6721

c)

std error=σx̅=σ/√n=0.14/√5 =

0.0626

probability =P(X<16)=(Z<(16-16.2)/0.063)=P(Z<-3.19)=0.0007

d)

std error=σx̅=σ/√n=0.14/√24 =

0.0286

probability =P(X<16)=(Z<(16-16.2)/0.029)=P(Z<-7)=0.0000