- #1
dirtybiscuit
- 8
- 1
Homework Statement
The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5.
a)if the distribution of all such pin hardness measurements is known to be normal, what is the probability that the average hardness for a random sample of 9 pins is at least 52.
b)what if sample is 40 pins?
Homework Equations
So I know that μ = 50 and σ(original) = 1.5, and n = 9
The Attempt at a Solution
σ(sample) = σ(original)/[itex]\sqrt{9}[/itex] = 1.5/3 = .5
now find P([itex]\bar{x}[/itex] > 52) by relating it to the standard normal dist
find z = (52 - 50)/.5 = 4.
This seems like a huge z score to have and it pretty much much makes the probability 0. Am I doing something wrong here? It just seems like a pointless question if in both cases the probability comes to zero.
Last edited: