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 0.6 years. He then randomly selects records on 37 laptops sold in the past. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected laptop is replaced more than 4.1 years? For 37 laptops, find the probability that the average replacement time is more than 4.1 year. For part d), is the assumption of normal necessary? NoYes
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
- What is the distribution of XX? XX ~ N(,)
- What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
- What is the
probability that one randomly selected laptop is replaced more than 4.1 years? - For 37 laptops, find the probability that the average replacement time is more than 4.1 year.
- For part d), is the assumption of normal necessary? NoYes
Sampling distribution of sample mean () :
If simple random sample of size n is drawn from Normal population with mean and standard deviation
(i.e. ) then sampling distribution of sample mean is approximately normal with mean and standard deviation
If population distribution is not normal then we need sample size greater than 30 to approximate Normal distribution.
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