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 1203992: 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 4.1 years and a standard deviation of 0.6 years. He then randomly selects records on 42 laptops sold in the past and finds that the mean replacement time is 3.8 years.
Find the probability that 42 randomly selected laptops will have a mean replacement time of 3.8 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 mean is 4.1
population standard deviation is .6
sample mean is 3.8
sample size is 42.
standard error = standard deviation / sqrt(sample size) = .6 / sqrt(42) = .092582.
z-score = (x - m) / s = (3.8 - 4.1) / .092582 = -3.240371.
x is the sample mean.
m is the population mean.
s is the standard error.
the probability of getting a z-score less than -3.240371 is .0005969333.
that's the probability of getting a sample mean less than 3.8.

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