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Solved: Emergency Room Visits The probability that a
Chapter 11, Problem 6RE(choose chapter or problem)
Visits The probability that a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05.
Source: SuperFreakonomics
(a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(b) What is the probability that fewer than 2 of 25 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(c) What is the probability that at least 2 of 25 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(d) What is the probability that at least 8 of 10 randomly selected visitors to the ER will not die within 1 year?
(e) Would it be unusual if more than 3 of 30 randomly selected visitors to the ER died within 1 year? Why?
(f) In a random sample of 1000 visitors to the ER, how many visitors are expected to die within the next year? What is the standard deviation number of deaths?
(g) At a particular emergency room, a researcher obtains a random sample of 800 visitors and finds that after 1 year 51 of them have died. Do you think this particular emergency room should be investigated to see if something unusual is occurring?
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QUESTION:
Visits The probability that a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05.
Source: SuperFreakonomics
(a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(b) What is the probability that fewer than 2 of 25 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(c) What is the probability that at least 2 of 25 randomly selected visitors to the ER will die within 1 year? Interpret this result.
(d) What is the probability that at least 8 of 10 randomly selected visitors to the ER will not die within 1 year?
(e) Would it be unusual if more than 3 of 30 randomly selected visitors to the ER died within 1 year? Why?
(f) In a random sample of 1000 visitors to the ER, how many visitors are expected to die within the next year? What is the standard deviation number of deaths?
(g) At a particular emergency room, a researcher obtains a random sample of 800 visitors and finds that after 1 year 51 of them have died. Do you think this particular emergency room should be investigated to see if something unusual is occurring?
ANSWER:
Step 1 of 7
Given: The probability that a randomly selected patient who visits the emergency room (ER) will die within 1 year of the visit is 0.05
a) probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year
n = 10, x = 1, p= 0.05 and 1-p = 0.95
\(P(x = 1) = nCx\ p^x\ (1-p)^{n-x}\)
\(= 10C1\ (0.05)^1\ (0.95)^9\)
\(= 10\ (0.05)\ (0.630)\)
\(P(x = 1) = 0.3151\)
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