I have a question on a hw problem.... If measurements of the specific gravity of

Question

I have a question on a hw problem.... If measurements of the specific gravity of a metal can belooked upon as a sample from a normal population having a standarddeviation of 0.04, what is the probability that the mean of arandom sample of size 25 will be "off" by at most 0.02? I have tried to work this problem several different ways to noavail. I'm assuming that to get the probability, we willeventually need Z values.  I assumed that 0.02 was thec.o.v. and had tried to use that to find xbar, but am not sureif I'm on the right track. Any help would beappreciated. I'd really like to understand how to work thisproblem. Thanks! I have a question on a hw problem.... If measurements of the specific gravity of a metal can belooked upon as a sample from a normal population having a standarddeviation of 0.04, what is the probability that the mean of arandom sample of size 25 will be "off" by at most 0.02? I have tried to work this problem several different ways to noavail. I'm assuming that to get the probability, we willeventually need Z values.  I assumed that 0.02 was thec.o.v. and had tried to use that to find xbar, but am not sureif I'm on the right track. Any help would beappreciated. I'd really like to understand how to work thisproblem. Thanks!

Explanation / Answer

SE(X bar) = SD / n = 0.04 / 25 =0.04 / 5 = 0.008
Error / SE(X bar) = 0.02 / 0.008 = 2.5 (Remember that the error can be positive or negative.) (Remember that the error can be positive or negative.) So you want to find P(-2.5 < Z < 2.5) =P(Z < 2.5) - P(Z < -2.5)     = 0.9938 - 0.0062= 0.9876 Hope this helps, Mike

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