The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.
A) .25
B) .75
C) 0
D) 1

Question

Quizplus · Accepted Answer

Since the assembly time is uniformly distributed between 6 and 10 minutes, we know that the probability of assembling the product in any given minute is the same. To find the probability of assembling the product in 7 minutes or more, we need to find the area of the shaded region in the following graph:

[graph of uniform distribution between 6 and 10 minutes, with shaded region between 7 and 10 minutes]

The total area under the graph is 1, since the probability of assembling the product in any amount of time between 6 and 10 minutes is 1. The area under the graph between 6 and 7 minutes is (7-6)/4 = 1/4, since the slope of the graph is constant over that interval. Therefore, the area under the graph between 7 and 10 minutes is 1 - 1/4 = 3/4. This means that the probability of assembling the product in 7 minutes or more is 3/4 or 0.75, which corresponds to choice B.

The Assembly Time for a Product Is Uniformly Distributed Between