An engineering development laboratory conducted an experiment to investigate the life characteristics of a new solar heating panel, designed to have a useful life of at least 5 years with probability. A random sample of 20 such solar panels was selected, and the useful life of each was recorded.

a. What is the probability that exactly 18 will have a useful life of at least 5 years?

b. What is the probability that at most 10 will have a useful life of at least 5 years?

c. If only 10 of the 20 solar panels have a useful life of at least 5 years, what would you infer about the true value of p?