Question

At an urgent care facility, patients arrive at an average rate of one patient every five minutes. Assume that the duration between arrivals is exponentially distributed. (Round your answers to four decimal places.)
a. Find the probability that the time between two successive visits to the urgent care facility is less than four minutes.

b. Find the probability that the time between two successive visits to the urgent care facility is more than 16 minutes.

c. If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the next nine minutes?

d. Find the probability that more than eight patients arrive during a half-hour period.

Answer 1

a)

To determine the probability that the time between two successive visits to the urgent care facility is less than four minutes

P(X < 4) = 1 - e^(-4/5)

= 1 - 0.4493

= 0.5507

b)

To give the probability that the time between two successive visits to the urgent care facility is more than 16 minutes

P(X > 16) = 1 - P(X < 16)

= 1 - (1 - e^(-16/5))

= 0.0408

c)

P(x > 19|x > 10) = P(x > 10+9|x > 10)

= P(x > 9)

= 1 - P(x <= 9)

= 1 - (1 - e^-9/5)

= e^(-9/5)

= 0.1653