Long-term history indicates that there is an average of 2.98 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 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 2.98 has 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 ad information. 12 13 2H 3 4 S or more (a) The pathologist wants to use a Poisson distribution to represent the probability of , the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = (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 given below. r! Here 1 = 2.98 is the average number of bacteria colonies per field. Compute P() for / = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) (b) Compute the expected number of colonies E = 100(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to one decimal place.) (c) Compute the sample statistic x2 = \\ (0 - E) and the degrees of freedom. (Round your test statistic to three decimal places.) E d. f 7 =