Quality Assurance: Mean Time Before Failure question

The MTBF of a system component is 2,500 cycles.  Using Table 3.2 and the equations provided in our textbook, set up your formulae and then answer the following questions:

a.   What is the probability that the component will not fail before 5,000 cycles?  What is the probability that the component will fail?


b.   What is the probability that the component will not fail before 10,000 cycles?  What is the probability that the component will fail?


Here is table 3.2 for reference.
Table 3.2: Values of e^-T/MTBF

T/MTBF      e^-T/MTBF
0.10         0.9048
0.50         0.6065
1.00         0.3679
1.50         0.2231
2.00         0.1353
2.50         0.0821
3.00         0.0498
3.50         0.0302
4.00         0.0183
4.50         0.0111
5.00         0.0067
5.50         0.0041
6.00         0.0025
6.50         0.0015