Among 100 purification filters used in an experiment, 46 had a service life of less than 20 hours, 19 had a service life of 20 or more but less than 40 hours, 17 had a service life of 40 or more but less than 60 hours, 12 had a service life of 60 or more but less than 80 hours, and 6 had a service life of 80 hours or more. Test at the 0.01 level of significance whether the lifetimes may be regarded as a sample from an exponential population with \(\mu=40\) hours.

Calculate \(P[0