In the US, the probability that a child dies in the first year of life is 0.0085.
In a certain rural county, for a recent year, 950 infants were born.
(For the sake of this exam, assume that these are all singleton births.)
18 of these infants died in their first year of life.
The county supervisors ask you if this indicates that the county's experience is different from that of the US population, if too many children are dying in their first year of life.
1. Explain what probability distribution you will use to assess these data, and exactly why. Discuss all relevant features and assumptions.
[Hint: It is not Poisson. We do not have anything like average rate of deaths per 100,000, or a fixed rate of deaths per period of time or area.
Set the problem up as having a sample size of 950.]
2. If the probability of dying in the first year of life for infants born in this county is the same as the US probability, what is the probability that 18 or more children of the 950 born would die in their first year of life? Give all details.
3. Based on your probability calculation, what you do conclude?