Exhibit 6-3.Patients scheduled to see their primary care physician at a particular hospital wait,on average,an additional eight minutes after their appointment is scheduled to start.Assume the time that patients wait is exponentially distributed. Refer to Exhibit 6-3.What is the probability a randomly selected patient will have to wait more than 10 minutes?
A)0.2865
B)0.4493
C)0.5507
D)0.7135

Question

Quizplus · Accepted Answer

The probability that a randomly selected patient will have to wait more than 10 minutes is 0.2865. This is because the exponential distribution is a continuous probability distribution that describes the time between events that occur at a constant average rate. The probability density function of the exponential distribution is given by:```f(x) = λe^(-λx)```where:* λ is the average rate of occurrence of events* x is the time between eventsIn this case, the average rate of occurrence of events is 1/8 minutes, since patients wait an average of 8 minutes after their appointment is scheduled to start. Therefore, the probability density function of the exponential distribution is:```f(x) = (1/8)e^(-1/8x)```The probability that a randomly selected patient will have to wait more than 10 minutes is given by the integral of the probability density function from 10 to infinity:```P(X > 10) = ∫[10,∞] (1/8)e^(-1/8x) dx = 0.2865```