Reliability of an MRI scanner. The reliability of a magnetic resonance imaging (MRI) scanner was modeled in Reliability Engineering and System Safety (January 2020) using a modified exponential distribution. Data indicated that the mean time between failures of the scanner was 40 days. Assume that x, the time (in days) between failures, is exponentially distributed with u = 40. Find the following probabilities.

a. P130 6 x 6 802.

b. P1x 7 1202.

c. P1x 6 502.