3. Robert Smith of the "Merrill Lynch Pierce Fenner & Smith" families is engaged in full-time fundraising. He has been quite successful at this because he brings a very structured approach to the process: you ask people directly and quickly for money. You don't waste your own time and you don't waste their time. His view is that in any relevant population there are about 10% of the people interested in your cause and, of that group, there are about 10% of those who are willing to give to it. The more people you talk to, the more people you're going to find that are willing to give. In raising money for the Orlando Symphony, he coordinated a campaign that identified as residents of Orlando as the relevant population to approach. Using his estimates of success, answer the following questions.
a. If you approached 100 Orlando residents, on average how many of them would be interested in the Orlando Symphony? How many, on average, willing to give money?
b. In a sample of 50 residents, what are the chances that 10 or more would be interested in the Symphony?
c. In a sample of 200 residents, you get the expected number who are interested in the Symphony; of that number, what is the probability that there are 5 willing to give money?
d. According to the 2000 U.S. Census, there are just over 100,000 adults in Orlando between the ages of 25 and 65 ("the giving years"). Using 100,000 as the potential number of givers, if the fundraising campaign generates the expected numbers of those interested and those who give and the average donation to the Symphony by a giver is $250, how much can this campaign expect to collect in donations?
Please see the attached file.
This is a binomial distribution where p=0.1 and q=0.9, n=50
We need to ...
The solution calculates the probabilities related to residents based on a US census in Orlando.