Question

The length of stay at a specific emergency department in a hospital in Los Angeles had a mean of 6.8 hours. Assume that the length of stay is exponentially distributed. What is the probability of a length of stay of more than 9 hours? State your answer in decimal format with 2 decimal

Answer 1

The probability of a length of stay of more than 9 hours at the emergency department is 41.9%.

Step-by-step explanation:

To find the probability of a length of stay of more than 9 hours at the emergency department, we need to use the exponential distribution formula. In this case, the mean is 6.8 hours. The equation for the exponential distribution is P(X > x) = e^(-lambda*x), where lambda is the rate parameter.

Since the mean is equal to 1/lambda, we can solve for lambda by taking the reciprocal of the mean: lambda = 1/6.8 = 0.1471.

Now, we can plug in the values into the equation to find the probability: P(X > 9) = e^(-0.1471*9) = 0.419.

Therefore, the probability of a length of stay of more than 9 hours is 0.419 or 41.9%.