Trenton Engineering has assigned seven engineers to work independently on a new product design. It is estimated that each engineer has a 65% chance of developing a design that is acceptable. How likely is it that Trenton ends up with
a. no acceptable designs?
b. at least three acceptable designs?
c. between two and four (inclusive) acceptable designs?
d. If Trenton wants to ensure that the probability of ending up with at least one acceptable design is more than 99%, what is the minimum number of engineers Trenton should assign to work on the product design? (Assume the 65% probability applies to each one.)