Plastic bags used for packaging produce are manufactured so that the breaking st

Question

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. a. If a sample of 25 bags is selected, what is the probability that the average breaking strength is between 5 and 5.5 pounds per square inch? b. If a sample of 25 bags is selected, what is the probability that the average breaking strength is less than 4.6 pounds per square inch? c. If a sample of 25 bags is selected, what is the probability that the average breaking strength is between 4.2 and 4.5 pounds per square inch?

Explanation / Answer

here for n=25; std error of mean =std deviation/(n)1/2 =0.3

for z =(X-mean)/std error

1) P(5<X<5.5)=P(0<Z<1.6667)=0.9522-0.5=0.4522

2)P(X<4.6)=P(Z<-1.3333)=0.0912

3)P(4.2<X<4.5)=P(-2.6667<Z<-1.6667)=0.0478-0.0038=0.0440

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