I've been faced with a question that I didn't really comprehend well, your assistance would be greatly appreciated. Here it is: "The life length X of an electronic component follows an exponential distribution. There are 2 processes by the component may be manufactured. The expected life length of the component is 100h if the process I is used to manufacture, while it is 150h if the process II is used. The cost of manufacturing a single component by process I is 10,whileits20' tabindex="0">,whileits20,whileits20 for process II. Moreover if the component last less than the guaranteed life of 200h, a loss of 50$ is to be borne by the manufacturer. Which process is advantageous to the manufacturer?"

So the way I understood the question is that I need to find the probability of the exponential distribution of both the 2 processes then compare the values and take the greater one. However, I can't seem to understand how to find (Lumbda) or the limits for the integration, and what to do with the numbers given in the question. Taking note that the formula for normal distribution given to us is as follows ( P(x=?)= Integrate( F(x)dx ) ) and (Lumbda=1/mean).

Would you please help me solve and better understand this question?