Final answer:
The probability that the commuting time will be less than 84 minutes is 0.8 or 80%.
Step-by-step explanation:
To find the probability that the commuting time will be less than 84 minutes, we need to find the area under the probability density function curve up to 84 minutes. Since the commuting time is uniformly distributed between 68 and 88 minutes, the total area under the curve is 1.
The width of the rectangle representing the probability density function is 88 - 68 = 20 minutes, and the height of the rectangle is 1/20 since the area under the curve must be 1. Therefore, the probability that the commuting time will be less than 84 minutes is the area of the rectangle up to 84 minutes, which is (84 - 68) * (1/20) = 0.8 or 80%.