Question

The time taken to assemble a machine in a certain plant is a random variable having a normal distribution of 32 hours and a standard deviation of 3.6 hours. What is the probability that a machine can be assembled at this plant in less than 25.4 hours?

(a) 0.61

(b) 0.674

(c) 0.298

(d) 1.823

I got this question during a job interview.

This intriguing question comes from Probability Distribution topic in section Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (c) 0.298

To elaborate: We have to find P(x < 25.4). Now, for x = 25.4, z becomes \(\frac{25.4 – 32}{3.6}\) = -1.83. Hence, P(z < -1.83) = 0.298.