The probability a randomly selected patient will have to wait more than 10 minutes is 0.550.
Given data;
An additional eight minutes are often added to the wait time for people who have appointments with primary care doctors at a specific hospital. Assume that patient wait times are distributed exponentially.
What is the likelihood that a randomly chosen patient will be kept waiting for longer than 10 minutes?
For exponentially distributed we use the formula as;
[tex]F(x) = 1 - e^-^x^/^\alpha[/tex]
Here, α = 8
x = 10
Now,
[tex]F(x) = 1 - e^-^x^/^\alpha[/tex]
[tex]F(x) = 1 - e^-^1^0^/^8[/tex]
[tex]F(x) = 1 - 0.449[/tex]
[tex]F(x) = 0.550[/tex]
Hence, the probability that a randomly chosen patient will be kept waiting for longer than 10 minutes is 0.550.
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