A review of emergency room records at hospital was performed to determine the probability distribution of the number of patients (X) entering the emergency room during a 1-hour period. The following table lists this probability distribution. x=x 0 1 2 3 4 5 6 Pr (x=x) 0.2725 0.3543 .2303 * 0.0324 0.0084 0.0023 Determine the probability that the number of patients entering the emergency room during a randomly selected 1-hour period is (a) Find the value of ‘*’.  (b) Determine P(1 ≤ ? < 4).  (c) Find E(X).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 2E
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QUESTION 1 
A review of emergency room records at hospital was performed to determine the probability
distribution of the number of patients (X) entering the emergency room during a 1-hour period. The
following table lists this probability distribution.

x=x 0 1 2 3 4 5 6
Pr (x=x) 0.2725 0.3543 .2303 * 0.0324 0.0084 0.0023


Determine the probability that the number of patients entering the emergency room during a randomly
selected 1-hour period is
(a) Find the value of ‘*’. 
(b) Determine P(1 ≤ ? < 4). 
(c) Find E(X).

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