The amount of air pressure, (PSI) in the spare tire of a certain vehicle (Type A) brought for inspection are normally distributed with PSI of µ = 30 and σ = 4, and such spares tires with PSI below 25 are considered under-inflated. The amount of air pressure, (PSI) in the spare tire of a certain vehicle (Type B) brought for inspection are normally distributed with PSI of µ = 27.7 and σ = 5.4, and such spare tires with PSI below 25 are considered under-inflated.
The PSI found in the spare tire of vehicle Type A and vehicle Type B does not depend upon the other type of vehicle, and every vehicle has 1 spare tire in it.
a. What is the probability that, for the next Type A vehicle and next Type B vehicle that are inspected, that BOTH vehicles have an under-inflated spare tire?
b. What is the probability that, for the next Type A vehicle and next Type B vehicle that are inspected, that there is a total of EXACTLY one under-inflated spare tire among these two vehicles?