Answer to Question #248754 in Statistics and Probability for Lazysloth

Question

The time it takes to assemble a car in a certain factory is a random variable with a mean of 20 hours and a standard deviation of 2 hours.
If 25 cars are assembled per day:
1. How many cars are assembled in less than 24 hours?
2. How many cars are assembled in atleast 22 hours?

Answer 1

Let $X=$ the time it takes to assemble a car in a certain factory: $X\sim N(\mu, \sigma^2).$  

Given $\mu=20\ h, \sigma=2\ h.$

$$P(X<24)=P(Z<\dfrac{24-20}{2})=P(Z<2)$$

$$\approx0.977250$$

$$P(X\geq22)=1-P(X<22)=$$

$$1-P(Z<\dfrac{22-20}{2})=1-P(Z<1)$$

$$\approx0.158655$$

1.

$$0.977250(25)=24(cars)$$

2.

$$0.158655(25)=4(cars)$$