## gabby817 2 years ago Please help me. A travel airline surveyed 950 business travelers 19% responded. What is the probability that more than 25% say that their travel was internal company visit

• This Question is Open
1. liza2

you didn't provide enough info to answer this.

2. gabby817

Travel weekly International air transport association survey asked business travelers about their purpose for their most recent business, trip. 19% respond that it was for an internal company visit. Suppose950 business travelers are randomly selected. What is the probability that more than 25% of the business tracers say that their most recent business trip was an internal company visit

3. queelius

This is probably a problem that can be solved more appropriately (and more effectively) using stats, but since I haven't taken stats in such a long time I don't feel inclined to solve it that way. I'm going to go with a pure probability (number of ways) approach -- I apologize to anyone reading this ahead of time. Imagine a branching tree, where each node in the tree can go in one of two directions with probability p = 0.19 that they take the outbound edge for "most recent business trip was an internal company visit" and otherwise they take the other edge with probability (1-p) = 0.81. If we do this for 950 people, and n of them took the p edge, and (950 - n) took the (1-p) edge, then the probability of that path through the tree is p^n * (1-p)^(950-n). A very low probability, to be sure, no matter what n is. So, now we want to figure out all the ways in which a path of n edges are the "p" edges, which is just (950 choose n) ways. So: (950 choose n) * [ p^n * (1-p)^(950-n) ] If we allow n to be a non-whole number (thanks to various extensions to the factorial, this is possible), then we can choose n to be a fraction equal to 950 * 0.25 = 237.5. So, the final equation is: (950 choose 237.5) * p^237.5 * (1-p)^(950 - 237.5) This will be a small number. I'm not sure it makes much sense, either. I think a more reasonably interpretation is to say, ok, we can't have 25% on the nose -- a person can't be divided. So, find a close whole number approximation, e.g., 238 people. In fact, we also don't want 25% on the nose, but rather in the range of 24.5% to 25.5%, being sure to round to the nearest whole numbers for the end-points -> 233 to 242 people. So, sum over this, e.g.: [sum from n = 233 to n = 242] (950 choose n) * [ p^n * (1-p)^(950-n) ] I'm sure this is a terrible approach, and there are statistical approaches that will deal with this problem much more effectively.