27. Peter, Paul, Mary, John and Martha are members of the pastoral council at a local church. They are to be seated at one side of a long conference table in a pastoral council meeting.a) How many possible ways can these 5 council members be seated?b) How many possible sitting arrangements are there if only gender is considered in the process?

28. How many social robots would need to be sampled in order to estimate the proportion of robots designed with legs, no wheels to within .075 of its true value with 99% confidence. Given that a random sample of 106 robots showed that 63 were designed with legs, no wheels.

29. Composite sampling is a way to reduce laboratory testing costs. A public health department is testing for possible fecal contamination in public swimming pools. In this case, water samples from 5 pools are combined for one test, and further testing is performed only if the combined sample shows fecal contamination. Based on past experience, there is a 3% chance of finding fecal contamination in a public swimming area. What is the probability that a combined sample from 5 swimming pools has fecal contamination? Recall that P(A) +P(not A) = 1.0.

Attachment:- 531666_1_STAT-230-Spring-2014-Final-Exam.pdf