A company wishes to study the number of credit applcations received
per day for the last 300 days.
Data:  # of Credit Applications         Frequency(number of days)
                 0                        50
                 1                        77
                 2                        81
                 3                        48
                 4                        31
                 5 or more                13
Would it be reasonalbe to conclude that the population distribution
isPoisson with a mean of 2.0?  Use the .05 significance level.  Find
the probability of exactly one success given a Poisson distribution
with a mean of 2.0.  Multiply this probability  by 300 to find the
expected frequency for the number of days in which there was exactly
one applications.  Determine hthe expected frequency for the other
days in a similar manner.

This sounds like homework.  See the FAQs.  So I'll just remind you of a few things.

See the link:

http://en.wikipedia.org/wiki/Poisson_distribution

In probability theory and statistics, the Poisson distribution is a
discrete probability distribution. It expresses the probability of a
number of events occurring in a fixed time if these events occur with
a known average rate, and are independent of the time since the last
event.

If the mean is an integer n, the most likely number of occurrences is
equally likely to be n and (n-1).

I forgot to add, for the Poisson distribution, the mean and variance are the same.