[Step-by-Step] ER Arrivals Consider the exponential density function discussed in Example 6: e(t)=0.2 e^-0.2 t \text when t ≥q 0 where t is the time


Question: ER Arrivals Consider the exponential density function discussed in Example 6:

\[e(t)=0.2 e^{-0.2 t} \quad \text { when } t \geq 0\]

where \(t\) is the time in minutes between successive arrivals at an emergency room in a large hospital on Saturday nights.

  1. Find the probability that successive arrivals are between 20 and 30 minutes apart.
  2. Find the probability that 10 minutes or less elapses between successive arrivals.
  3. Find the probability that successive arrivals will be more than 15 minutes apart.

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