I know you are probably not able to use R to compute the numerical answer, but h
ID: 3048369 • Letter: I
Question
I know you are probably not able to use R to compute the numerical answer, but how would you answer the rest of the questions/ what would you do for the equations for the R problems?
Coal mining is a dangerous job. For each of the years 2006-2015, the number of accidental coal mining deaths (on the job) is given 47 34 30 18 48 20 20 20 16 11 For perspective, there are about 83,000 full time coal miners in the United States. Based on this information, a.) estimate the probability that the year 2016 will see at least 20 coal mining accidental deaths? Be sure to write an expression for the probability, then have R compute it. b.) similarly estimate the probability that there will be at least 120 deaths in the five-year window 2016-2020.Explanation / Answer
a. The number of deaths from the year 2006 to 2015 are as follows:
47 34 30 18 48 20 20 20 16 11
These are a set of 10 observations, and we want to predict outcome of the of the deaths in the year 2016
So we will have to first find the sample space for the defined situation
Situation is at least 20 deaths in 2016, so in the last 10 years there are 7 observations that have at least 20 deaths, so we can calculate the probability as 7/10 = 0.7
So the probability that we see at least 20 deaths in 2016 is 0.7
An expression to calculate this would be x/10 where x is the number of obervations in the sample space,
To compute the number of observations in the sample sapce using R we will use this code
deaths <- c(47,34,30,18,48,20,20,20,16,11)
x<- len(deaths[deaths>=20])
prob < - x/10
b. Prob that there will be at least 120 deaths in the five year window 2016-2020 is that same prob of having at least 24 deaths in each year and there are 4 observation in the last 10 years where we have more than 24 deaths
Hence prob of having 24 deaths in a year = 4/10 =0.4
So prob of having at least 120 deaths in 5 year window = 0.4 x 0.4 x 0,4 x 0.4 x 0.4 = 0.4^5 = 0.01 = 1 / 100
So there is a 1% chance that there will be at least 120 deaths in the next 5 years