A club is holding a raffle. Ten thousand tickets have been sold for $2 each. There will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each and 20 consolation prizes of $100 each. Find the expected winnings of a single ticket. ​

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).