4.11. What is the probability of obtaining exactly 6 events for a Poisson distribution with parameter μ = 4.0?

4.12. What is the probability of obtaining at least 6 events for a Poisson distribution with parameter μ = 4.0?

4.13. What is the expected value and variance for a Poisson distribution with parameter μ = 4.0?

Newborns were screened for human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) in five Massachusetts hospitals. The data [8] are shown in Table 4.14.

4.14 (use computer) If 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of 5 HIV-positive test results?

4.15 (use computer) If 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of at least 5 HIV-positive test results?

4.16 Answer Problems 4.14 and 4.15 using an approximation rather than an exact probability.

Many investigators have suspected that workers in the tire industry have an unusual incidence of cancer.

4.23 Suppose the expected number of deaths from bladder cancer for all workers in a tire plant on January 1, 1964, over the next 20 years (1/1/64–12/31/83) based on U.S. mortality rates is 1.8. If the Poisson distribution is assumed to hold and 6 reported deaths are caused by bladder cancer among the tire workers, how unusual is this event?

4.24 Suppose a similar analysis is done for stomach cancer. In this plant, 4 deaths are caused by stomach cancer, whereas 2.5 are expected based on U.S. mortality rates. How unusual is this event?

An important issue in assessing nuclear energy is whether excess disease risks exist in the communities surrounding nuclear-power plants. A study undertaken in the community surrounding Hanford, Washington, looked at the prevalence of selected congenital malformations in the counties surrounding the nuclear-test facility [9].

4.52 Suppose 27 cases of Down’s syndrome are found and only 19 are expected based on Birth Defects Monitoring Program prevalence estimates in the states of Washington,

Idaho, and Oregon. Are there significant excess cases in the area around the nuclear-power plant?

Suppose 12 cases of cleft palate are observed, whereas only 7 are expected based on Birth Defects Monitoring Program estimates.

4.53 What is the probability of observing exactly 12 cases of cleft palate if there is no excess risk of cleft palate in the study area?

4.54 Do you feel there is a meaningful excess number of cases of cleft palate in the area surrounding the nuclear power plant? Explain.

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