When Finn and Jake play Card Wars, Jake wins 80% of the time. They decide to have a best-of-7 Card Wars series to determine who is the Cool Guy, where they will play until one of them has won 4 games. That is, they will play at least 4 games (in the case that one player wins the first 4 in a row) and at most 7 games (in the case that they are tied 3 games to 3 after the first 6 games). What is the probability Jake wins after exactly 6 games

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).