Final answer:
To find the probability that the component lasts for more than 3 years, calculate the z-score and use the standard normal distribution table or a calculator.
Step-by-step explanation:
To find the probability that the component lasts for more than 3 years, we need to first find the z-score for 3 years using the formula:
z = (x - μ) / σ
where x is the value we are interested in (3 years), μ is the mean (2,400 hours), and σ is the standard deviation (300 hours).
Once we have the z-score, we can use the standard normal distribution table or a calculator to find the corresponding probability. The probability of the component lasting more than 3 years is the complement of the probability of it lasting less than or equal to 3 years.