5) Suppose 40% of all patients admitted to an emergency room are heart related patients. In a sample of 1000 patients, find the probability that at least 500 patients are heart related patients. approximately
5) Suppose 40% of all patients admitted to an emergency room are heart related patients. In a sample of 1000 patients, find the probability that at least 500 patients are heart related patients. approximately
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![5) Suppose 40% of all patients admitted to an emergency room are heart
related patients. In a sample of 1000 patients, find the probability
approximately that at least 500 patients are heart related patients.
Let X = # of patients (out of 1000) admitted due to heart related
disease
Then X ~ binomial (1000, 0.40)
Based on normal approximation X~ N(np, √np(1-p))
Mean np = 1000 * 0.40 = 400
St.Dev. √np(1-p) = √1000 * 0.0.40 * 60 = 15.49
Thus, X N(400, 15.49)
P(X ≥ 500) ≈ P(X≥ 499.5) - continuity correction
= normcdf(low-499.5, high-1000, mean-400, sig-15.49)
= 6.69 * 10-11 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f1fd340-6178-454b-aea7-37c134c266b7%2F0a0aff22-bdda-4c83-abe8-b57070ea14ee%2F6e1joqp_processed.png&w=3840&q=75)
Transcribed Image Text:5) Suppose 40% of all patients admitted to an emergency room are heart
related patients. In a sample of 1000 patients, find the probability
approximately that at least 500 patients are heart related patients.
Let X = # of patients (out of 1000) admitted due to heart related
disease
Then X ~ binomial (1000, 0.40)
Based on normal approximation X~ N(np, √np(1-p))
Mean np = 1000 * 0.40 = 400
St.Dev. √np(1-p) = √1000 * 0.0.40 * 60 = 15.49
Thus, X N(400, 15.49)
P(X ≥ 500) ≈ P(X≥ 499.5) - continuity correction
= normcdf(low-499.5, high-1000, mean-400, sig-15.49)
= 6.69 * 10-11 0
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