Question

The time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. what is the the probability it takes between 45.5 and 54.4 min. round to 4 decimal places. p(45.5 < x < 54.4) =

a) 0.3333
b) 0.4444
c) 0.5556
d) 0.6667

Answer 1

To find the probability that the task takes between 45.5 and 54.4 minutes in a continuous uniform distribution, we need to calculate the area under the probability density function (PDF) curve within this range. The probability is the ratio of the area within the range to the total area.

Step-by-step explanation:

To find the probability that the task takes between 45.5 and 54.4 minutes, we need to calculate the area under the probability density function (PDF) curve within this range.

Since the distribution is continuous and uniform, the PDF is a straight line with a constant height between the minimum and maximum values. The total area under the PDF curve is 1.

The probability between 45.5 and 54.4 minutes is the ratio of the area within this range to the total area.

Probability = (54.4 - 45.5) / (57 - 43) = 0.1667

Therefore, the probability that it takes between 45.5 and 54.4 minutes is approximately 0.1667.