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 4.3 years and a standard deviation of 0.5 years. He then randomly selects records on 35 laptops sold in the past. Round the answers of following questions to 4 decimal places.
a. What is the distribution of $X$ ? $X \sim \mathrm{N}($
b. What is the distribution of $\bar{x} ? \bar{x}-\mathrm{N}($
c. What is the probability that one randomly selected laptop is replaced less than 4.2 years?
d. For 35 laptops, find the probability that the average replacement time is less than 4.2 year.
e. For part d), is the assumption of normal necessary? No Yes
Answer
The replacement times for the model laptop of concern, represented by X, are normally distributed with a mean of 4.3 years and a standard deviation of 0.5 years. Therefore, the distribution of X is \(X \sim \mathrm{N}(4.3, 0.5^2)\).
Step 1 ：The replacement times for the model laptop of concern, represented by X, are normally distributed with a mean of 4.3 years and a standard deviation of 0.5 years. Therefore, the distribution of X is \(X \sim \mathrm{N}(4.3, 0.5^2)\).
