A laborer of an industry uses bus or train to reach the industry. The ratio of using bus and train is 3:7. The probability that the laborer
reaches to the industry late is 0.25 if he uses bus and the same
probability if he uses train is 0.05. One day he reaches to the
industry late. Find the probability that he uses train or bus.

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).