Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the surface of the mineral. A certain mineral specimen is of such an age that there should be an average of 6 tracks per cm² of surface area. Assume the number of tracks in an area follows a Poisson distribution. Let X represent the number of tracks counted in 1 cm² of surface area. Find

a. P(X = 7)

b. P(X ≥ 3)

c. P(2 < X < 7)

d. μ_X

e. σ_X