Final answer:
The proportion of lightbulbs that will last more than 61 hours according to the given data is approximately 89.6%.
Step-by-step explanation:
To find the proportion of lightbulbs that will last more than 61 hours, we need to use the exponential distribution with a mean lifetime of eight years.
Let's convert 61 hours to years by dividing it by 365 (number of days in a year), which gives us approximately 0.0667 years.
The probability that a lightbulb lasts less than one year can be found using the exponential distribution formula: P(X < x) = 1 - e^(-λx), where λ is the rate parameter. In this case, λ = 1/8 since the mean lifetime is eight years. So, P(X < 1) = 1 - e^(-1/8) ≈ 0.104
Therefore, the proportion of lightbulbs that will last more than 61 hours is approximately 1 - 0.104 = 0.896, or 89.6%.