Question

Probability Experts Needed! Topic: Central Limit Theorem

Answer 1

Problem:

The fracture strength of a certain type of glass has been found to have a standard deviation of approx 0.4 thousands of pounds per square inch. If the fracture strength of 100 pieces of glass is to be tested, find the approximate probability that the sample mean is within 0.2 thousands of pounds per square inch of the true population mean.

Attempt:

So, I understand that as sample sizes increase toward very large numbers (say, n = sample size approaches 100, or even infinity....), the distribution tends toward the standard normal distribution. This allows me to find the probability using the Z table for standard normal distribution.

I believe the formula to find Z is:\[Z=\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n}}}\]
However, I'm not sure how to apply that to this problem, as the sample mean is within 0.2 thousands of pounds per square inch, which suggests to me that the problem is actually asking the probability that the sample mean is within its standard deviation of 0.4.

\(\bar X\) is not given, so I don't think I need the above formula.

What do I do?


The question is asking for the probability that the to be asking for

Answer 2

Disregard the last incomplete sentence...

Answer 3

you just need to consider both directions

Answer 4

CLT still applies

Answer 5

So I need to find P(---something here < Z < ----something else here)

Answer 6

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