A pathologist has been studying the frequency of bacterial colonies within the fi­eld of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per fi­eld. Let r be a random variable that represents the number of bacteria colonies per fi­eld. Let O represent the number of observed bacteria colonies per fi­eld for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information.

(a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per fi­eld. The Poisson distribution is

Where l = 2.80 is the average number of bacteria colonies per fi­eld. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more.

(b) Compute the expected number of colonies E = 100P(r) for r = 0, 1, 2, 3, 4, and 5 or more.

(c) Compute the sample statistic

And the degrees of freedom.

(d) Test the statement that the Poisson distribution fi­ts the sample data. Use a 5% level of signi­ficance.

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2 5 or more 0 12 5 29 18 19 P(r) = (0 - E)2