A Harris Interactive survey for InterContinental Hotels & Resorts asked ...

     1. A Harris   Interactive survey for InterContinental Hotels & Resorts asked   respondents, “When traveling internationally, do you generally venture out on   our own to experience culture, or stick with your tour group and   itineraries?” The survey found that 23% of the respondents stick with their   tour groups.   a. In a sample of 6 international   travelers, what is the probability that two will stick with their tour group?   b. In a sample of 6 international   travelers, what is the probability that at least two will stick with their   tour group?   c. In a sample of 10 international   travelers, what is the probability that none will stick with their tour   group?                  2. The Poisson distribution is a   probability distribution that describes a pattern of behavior when some event   occurs at varying, random intervals over a continuum of time, length, or   space. Below is an example of the use of Poisson distribution.   The Elazar Rape Crisis Center wants to   staff its crisis hot line so that a center member will always be present if a   rape victim calls. The Crisis Center operates between the hours   of 6:00pm and 6:00am. By examining the past records of the center, the   director has determined that the mean number of rapes per hour is .05. This   information can be determined from police records.   Suppose that the director believes that   (based on past experience) assisting a rape victims takes about 4 hours. One   crisis center staff member remains with the victim for this period to assist   with the medical treatment and police procedures. If the center had one staff   member and two rapes occurred in a 4-hour period, then no one would be at the   center to assist the second victim. The director wants to avoid this   situation.    The 12-hour operating time is equivalent   to three 4-hour periods. If the probability of no one assisting a victim is   larger than 3% during these 12 hours is unacceptable. How many   staff member should be at the center during the office hours?