Final answer:
To find the probability that the time between two successive visits to the urgent care facility is less than two minutes, we need to calculate the cumulative distribution function (CDF) of the exponential distribution. To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution with the rate of events as lambda.
Step-by-step explanation:
To find the probability that the time between two successive visits to the urgent care facility is less than two minutes, we need to calculate the cumulative distribution function (CDF) of the exponential distribution. The CDF of the exponential distribution is given by F(x) = 1 - e^(-lambda*x), where lambda is the rate parameter and x is the time.
To find the probability that the time between two successive visits is less than two minutes, we need to calculate F(2). Substitute lambda = 1/7 and x = 2 into the CDF formula and calculate the result.
To find the probability that the time between two successive visits is more than 15 minutes, we need to calculate 1 - F(15), where F(x) is the CDF of the exponential distribution. Substitute lambda = 1/7 and x = 15 into the CDF formula and calculate the result.
To find the probability that the next person will arrive within the next five minutes, we need to calculate P(T < 5 | T > 10) using the conditional probability formula, where T is the time between two successive visits. We can use the following formula to calculate the conditional probability: P(A | B) = P(A ∩ B) / P(B). Substitute lambda = 1/7 into the PDF formula and use the formula to calculate the result.
To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution. The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space. The mean of the Poisson distribution is given by lambda, the rate of the events.
The complete question is: The following table lists the probability distribution of the number of patients entering the emergency room during a 1-hour period at Millard Fillmore Memorial Hospital. is: