Question

The time taken to assemble a car at the OKCar plant is a randomly distributed with a mean of 20.1 hours and a standard deviation of 2.3 hours. You pick a random sample of 30 cars. What is the probability that the mean number of hours that it took to assemble these 30 cars is between 19.8 and 20.8 hours?

Answer 1

Solution :

= / n = 2.3 / 30 = 0.4199

= P[(19.8 - 20.1) / 0.4199 < ( - ) / < (20.8 - 20.1) / 0.4199)]

= P(-0.71 < Z < 1.67)

= P(Z < 1.67) - P(Z < -0.71)

= 0.9525 - 0.2389

= 0.7136

Probability = 0.7136