Final answer:
The lifetime that is exceeded by 99% of lasers is approximately 13.4895 years. The mean lifetime of the lasers is 10 years and the variance is 100 years^2.
Step-by-step explanation:
The lifetime of lasers can be represented by an exponential distribution, which means that a certain percentage of lasers will have a lifetime less than or equal to a specific value. In this case, we are looking for the lifetime that is exceeded by 99% of lasers. To calculate this, we can use the inverse normal distribution function.
First, we need to find the Z-score corresponding to the 99th percentile. Using the formula NORMSINV(0.99), we get -2.3263. Next, we need to find the lifetime that corresponds to this Z-score. We know that the mean lifetime is 10 years, so we can calculate the standard deviation by multiplying the Z-score by the standard deviation and adding it to the mean.
Using the formula 2.3263 * 1.5 + 10, we get approximately 13.4895 years. Therefore, the lifetime that is exceeded by 99% of lasers is around 13.4895 years.
To find the mean and variance of the lifetime, we need to use the formulas for the mean and variance of an exponential distribution. For an exponential distribution with parameter λ, the mean is given by 1/λ and the variance is given by 1/λ^2. In this case, the mean lifetime is 10 years, so λ = 1/10. Therefore, the mean is 1/(1/10) = 10 years and the variance is 1/(1/10)^2 = 100 years^2