Please Do not skip Parts( if you cnnot do them all , leave it alone for someone
ID: 3270654 • Letter: P
Question
Please Do not skip Parts( if you cnnot do them all , leave it alone for someone else) Thank you
Part 1.deaths of infants in the US in the first year of life (9 points)
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 question, 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. (4 points) Explain what probability distribution you will use to assess these data, and exactly why. Discuss all relevant features and assumptions.
2. (3 points) 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. (2 points) Based on your probability calculation, what you do conclude?
Write a summary sentence for the county supervisors.
Explanation / Answer
1. We will use binomial distribution as the number of infants and the probability of their death is given so. it satisfy two parameter condition are fulfilled. but as the sample size is large, we will use normal aprroximation to binomial.
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,
Pr (NUmber of children dying >= 18) = ?
Where the expected number of children dying = 950 * 0.0085 = 8.075
Standard deviation of the number of children dying out of 950 children = sqrt [ 950 * 0.0085 * 0.9915] = 2.83
so Pr (NUmber of children dying >= 18, 8.075, 2.83) = ?
Z = (18 - 8.075)/ 2.83 = 3.51
so P - value = 1 - 0.9998 = 0.0002
3. based on the above p - value, we can conclude that the country's experience with infant mortality rate is different from the US national infant mortality rate.