raliubin sainpie ors / i patients when 15. (d) Explain how these calculations pr
ID: 3362844 • Letter: R
Question
raliubin sainpie ors / i patients when 15. (d) Explain how these calculations prov rate at this hospital is higher than the national rate. ide strong evidence that the true underlying death (e) Suppose I continue to observe heart transplant operations at this hospital until the next death. What is the probability that there will be 0 successful operations before this first death? Five successful operations? () What is the probability that there will be 10 successful operations before the 2d death? (g) Consider selecting 10 operations from the 371 in this time period which saw 79 deaths. What is the probability that we will see 8 or more deaths in our sample of 10? Hint: Define the random variable. Is this a "Bernoulli" process? (h) What if we had used the binomial probability distribution to calculate this probability? (i) Suppose the probability of a heart transplantation death in the general population is 0001. What is the probability that of at least one such death in a random sample of 5000Explanation / Answer
a)
Probability distribution is binomial with parameter - proportion 'p'
p = 0.15
b)
P(X >= 8) = =1 - BINOM.DIST(7,10,0.15,TRUE)
= 0.0000087
d)As we see probability of 8 and more deaths under the normal death rate is much lower than the actual observed rate of 80%.
This provides the strong reason.
e)
If we consider the death rate of 80% i.e. p=0.8
P(X = 0) = 0.8
P(X = 5) = (0.2)^5 * 0.8 = 0.000256
f)
P(X = 10) = (0.2)^10 * 0.8 = 0.00000008
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