Question

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean m = 6.3 minutes and standard deviation s = 2.2 minutes. For a door selected at random, what is the probability that the assembly-line time will be between 6 and 8 minutes?

Group of answer choices

A) 0.1

B) 0.21

C) 0.334

D) 0.67

Answer 1

Solution :

P(6 < x < 8) = P[(6 - 6.3)/ 2.2) < (x - $\mu$ ) /$\sigma$  < (8 - 6.3) / 2.2) ]

= P(-0.1364 < z < 0.7727)

= P(z < 0.7727) - P(z < -0.1364)

= 0.7801 - 0.4458

= 0.334

Probability = 0.334

option c)