Question 1203972
population replacement times mean is 4.3 years with a standard deviation of .6 years.


sample size of 54 laptops has a mean replacement time of 4.1 years.


z-score is used since stanard deviation is taken from the population and sample size is sufficiently large.


since mean of sample is being measured, standard error is used instead of standard deviation.
standard error = population standard devation divided by square root of sample ize = .6 / sqrt(54) = .081650.


z = (x - m) / s
z is the z-score
x is the sample mean
m is the population mean
s is the standard error


formula becomes z = (4.1 - 4.3) / .081650 = -2.449479.
area to the left of that = .007153.
that's the probability that he wil get a z-score of -2.449479 which is also the probability that he will get a sample with a mean less than 4.1 with the same sample size.


here's what it looks like on the calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


<img src = "http://theo.x10hosting.com/2023/093001.jpg">