Write each description using probability notation. 6. the probability of flipping tails for a coin flip 7. the probability of rolling a sum of 12 on two six-sided number cubes 8. the probability of not rolling a sum of 12 9. the probability of a spinner landing on an orange area 10. the probability of drawing a tile with the letter R from a bag​

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).