Using binomial distribution where success is the appearing of any of the top 10 most common names, thus probability of success (p) is 9.6% = 0.096 and the probability of failure = 1 - 0.096 = 0.904. Number of trials is 11.
Binomial distribution probability is given by P(x) = nCx (p)^x (q)^(n - x)
Probability that none of the top 10 most common names appears is P(0) = 11C0 (0.096)^0 (0.904)^(11 - 0) = (0.904)^11 = 0.3295
Thus, the probability that at least one of the 10 most common names appear is 1 - 0.3295 = 0.6705
Therefore, I will be supprised that none of the names of the authors were among the 10 most common names given that the probability that at least one of the names appear is 67%.
Answer :
The slope of the line is 0
X - Linda's speed
(x+8 )- Colleen's speed
8x - Linda's distance for 8 h
8(x+8) = 8x+64 - Colleen's distance for 8 h
8x + 8x + 64 = 176 - distance between Colleen and Linda after 8 h
8x + 8x + 64 = 176
16x +64 = 176
16x = 176 - 64
16x = 112
x= 7 mph Linda's speed
x+8 = 7+8 = 15 mph Colleen's speed
