Answer Happy

A jeweler has 11 real gems and 7 fake gems. A sample of 6 of these will be selected at random for a display. Find the: a) probability that 4 or fewer of the gems selected will be real; b) the standard deviation in the number of real gems in the sample. Sheryl estimates that Jason makes approximately 2 errors per inch of parchment on all his essays. a) If Professor Calcaterra assigns a 15-inch, find the expected number of errors and the standard deviation in the number of errors in Jason's essay. b) Find the probability Jason makes exactly 12 errors in an 8 inch essay. c) Jason writes a new 8-inch essay every week day for four weeks (20 days). Find the probability that Jason makes exactly 12 errors on fewer than four days. (Note: this is a binomial problem with p equal to your solution in part (b)).