A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated.

a. What is the probability mass function of the number of opponents contested in a game?
b. What is the probability that a player defeats at least two opponents in a game?
c. What is the expected number of opponents contested in a game?
d. What is the probability that a player contests four or more opponents in a game?
e. What is the expected number of game plays until a player contests four or more opponents?

(a.s."similarity in right triangles"solve for xa.) 10b.) 20c.) 14.5d.) [tex] 6\sqrt{3} [/tex]

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? why? a. the z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. b. the z score of 0 is most preferable because it corresponds to a test score equal to the mean. c. the z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. d. the z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average

The table below shows the approximate masses of a dust particle and a grain of pollen. dust particle 0.000000778 g grain of pollen 0.00000000155 g the mass of a dust particle can be estimated and written in the form a × 10^b, where a = 8 and b = the mass of a grain of pollen can be estimated and written in the form a × 10^b, where a = 2 and b = based on the estimates, the mass of a dust particle is approximately blank times larger than the mass of a grain of pollen.