SOLUTION: The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement ti

Question 1203972: The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.3 years and a standard deviation of 0.6 years. He then randomly selects records on 54 laptops sold in the past and finds that the mean replacement time is 4.1 years.
Find the probability that 54 randomly selected laptops will have a mean replacement time of 4.1 years or less. Round your answer to four decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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 https://davidmlane.com/hyperstat/z_table.html

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