Question 1164887: The manager of a computer retails 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 4.2 years and a standard deviation of 0.4 years. He then randomly selects records on 38 laptops sold in the past. Round the answers of following questions to 4 decimal places.
What is the distribution of X?X~ N(_______,_________)
What is the distribution of ¯x?¯x~ N(________,_________)
What is the probability that one randomly selected laptop is replaced more than 4.3 years?
For 38 laptops, find the probability that the average replacement time is more than 4.3 year.
For part d), is the assumption of normal necessary? Yes or No
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x ~ N(4.2, 0.16)
x bar ~ N(4.2, 0.16/38) or ~N(4.2, 0.0042)
z>(4.3-4.2)/0.4 or >0.25. That probability is 0.4013
z>(4.3-4.2)/(.4/sqrt38) or 0.0649 or z>1.54 or 0.0616
Yes, the assumption is necessary since the approach to doing so requires normality. It this were not the case, a non-parametric approach would be used.
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