A supplier to a car manufacturer produces a certain valve and seal used in their cars. The sizes of these seals and valves are closely monitored to ensure the parts actually work. Here are summary statistics on
the diameters for these valves and seals (in millimeters).
Mean
Standard deviation
Valve
Hy = 50
Oy = 0.3
Seal
His = 51
Os = 0.4
Both distributions are approximately normal. A seal properly fits a valve if the seal's diameter is larger than
the valve's diameter, but the difference can't be more than 2 mm. Suppose we choose a valve and seal at
random and calculate the difference between their diameters. We can assume that their diameters are
independent.
Find the probability that the seal properly fits the valve.
You may round your answer to two decimal places.
P (proper fit)