Question 1205164
mean is 8.4 hours
standard deviation is 1.8 hours.
probability of randomly selected mechanic has a rebuild time greater than 8 hours?
use the z-score.
z = (x-m)/s
z is the z-score
x is the random mechanic time.
m is the mean
s is the standard deviation.
formula becomes z = (8 - 8.4) / 1.8 = -.2222
area to the right of that z-score is equal to .5879.
that's the probability that the randomly selected mechanic will take more than 8 hours to rebuild the transmission.
here's what it looks like on a graph using z-scores.


<img src = "http://theo.x10hosting.com/2023/112902.jpg">


here's what it looks like on a graph using raw scores.


<img src = "http://theo.x10hosting.com/2023/112901.jpg">


when using z-scores, the mean is 0 and the standard deviation is 1.


when using raw scores, the mean is what it is and the standard deviation is what it is .


the calculator that generated that graph can be found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>