Question

The time taken to assemble a car in a certain plant is a random variable having a normal

distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a

car can be assembled at this plant in a period of time less than 19.5 hours?

Answer 1

$P\left( X<19.5 \right) =P\left( \frac{X-20}{2}<\frac{19.5-20}{2} \right) =\varPhi \left( -0.25 \right) =0.401$