stats... bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1 ..

Question

Plastic bags used for packaging produce are manufactered 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. If a sample of 25 bags is selected, what is the probability that the average breaking strength is a) between 5 and 5.5 pounds per square inch? b)between 4.2 and 4.5 pounds per square inch? c)less than 4.6 pounds per square inch? d)between what two values symmetrically distributed around the mean will 95% of the average breaking strengths fall? First one to answer correctly gets 10 pts!

Answer 1

By the central limit theorem, the standard deviation for the sample of 25 is 1.5/5=.3
a) small z=0 and large z=(5.5-5)/.3=.166
answer = .0661
b) zsmal=(4.2-5)/.3=-2.66 and z big= (4.5-5)/.3=-1.66
answer=.044
c) zlarge=(4.6-5)/.3=-1.33, zsmall=-infinity
answer= .091