The time to failure, t, in hours, of a machine is often

Last updated: 8/9/2022

The time to failure, t, in hours, of a machine is often exponentially distributed with a probability density function f(t) = ke⁻ᵏᵗ, 0≤t<∞, where k=1/a and a is the average amount of time that will pass before a failure occurs. Suppose that the average amount of time that will pass before a failure occurs is 100 hr. What is the probability that a failure will occur in 58 hr or less? The probability is____ (Round to four decimal places as needed.)