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The mean number of newly diagnosed syphilis cases in Iowa during 2019 was 1.7 cases per...

The mean number of newly diagnosed syphilis cases in Iowa during 2019 was 1.7 cases per week. Assume that this weekly average still holds. For a given week, let S represent the number of new syphilis cases diagnosed in Iowa.

a) S is the number of events that take place over a certain interval of time. What type of probability distribution might S have? Assuming that S has this distribution, what would be the mean of S, and the variance of S?

b) Find the probability that exactly four new cases of syphilis will be diagnosed in Iowa during the week of interest. (Include probability notation, calculations, and final answer to 3 decimal places.)

Math   Statistics-And-Probability   
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Answer #1

a) S is the number of events that take place over a certain interval of time. What type of probability distribution might S have?

S might have the poisson distribution with = 1.7

Assuming that S has this distribution, what would be the mean of S, and the variance of S?

The mean of poisson distribution is = 1.7

The variance of poisson distribution is = 1.7

b) Find the probability that exactly four new cases of syphilis will be diagnosed in Iowa during the week of interest.

We need to compute \Pr( X = 4) . Therefore, the following is obtained:

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