Q1. The probability that an individual egg in a carton of eggs is cracked is 0.03. You havepicked out a carton of 1 dozen eggs (that's 12 eggs) at the grocery store. Determine the probability that at most one of the eggs in the carton are cracked.
Q2. Peter, Paul, Mary, John and Martha are members of the pastoral council at a localchurch. They are to be seated at one side of a long conference table in a pastoral councilmeeting.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 theprocess?
Q3. How many social robots would need to be sampled in order to estimate the proportion ofrobots 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 designedwith legs, no wheels.
Q4. Composite sampling is a way to reduce laboratory testing costs. A public healthdepartment is testing for possible fecal contamination in public swimming pools. In thiscase, water samples from 5 pools are combined for one test, and further testing isperformed only if the combined sample shows fecal contamination. Based on pastexperience, there is a 3% chance of finding fecal contamination in a public swimmingarea. What is the probability that a combined sample from 5 swimming pools has fecalcontamination? Recall that P(A) +P(not A) = 1.0.
Q5. A random sample of five accidents resulted in the following number of persons injured: 18, 15,12, 19, & 21. Using the .01 significance level, can we conclude the population mean is less than 20for all accidents?a) State Ho and Ha?b) Test statistic = ?c) Critical value = ?d) Reject Ho: (yes or no)