A synthetic fiber used in manufacturing carpet as tensile strength that is normally distributed with mean 75.5 psi & std dev 3.5 psi. Find the probability that a random sample of n=6 fiber specimens will have sample mean tensile strength that exceeds 75.75 psi. Consider the synthetic fiber in the previous exercise. How is the standard deviation of the sample mean changed when the sample size is increase from n=6 to n=49? What is the probability that the random sample of n=49 fiber specimens will have sample mean tensile strength that exceeds 75.75 psi?

Question

anonymous · Answer

I have already found the Probability and is equal to 0.4325, anyone help me out with second part plz

anonymous · Answer

@TuringTest

turingtest · Answer

sorry, this is just a bit beyond where I'm at in probability right now. Hopefully I'll know it in a few weeks.

anonymous · Answer

@dumbcow

dumbcow · Answer

the standard deviation of sample mean is
$$\frac{\sigma}{\sqrt{n}}$$
if n goes from 6 to 49 then standard deviation will get much smaller and probability of being greater than 75.75 will also be smaller