Understanding Uniform Distribution and Probability

This video tutorial explains how to determine probabilities involving a uniform distribution. It provides two examples: one for Worker 1, whose task completion time is uniformly distributed between 10 and 16 minutes, and another for Worker 2, with a distribution between 11 and 16 minutes. The video demonstrates two methods for calculating probabilities: using a fraction bar and calculating the area of a rectangle. The tutorial also explains how to express probabilities as simplified fractions and decimals.

What is the range of time for which worker 1's task completion is uniformly distributed?

• 5 to 15 minutes

• 10 to 16 minutes

• 12 to 18 minutes

• 8 to 14 minutes

How is the probability density function represented for a uniform distribution?

• A horizontal line

• A diagonal line

• A curved line

• A vertical line

What fraction represents the probability of worker 1 completing the task between 11 and 13 minutes using the fraction method?

• 1/4

• 1/3

• 1/2

• 2/3

What is the simplified decimal form of the probability that worker 1 completes the task between 11 and 13 minutes?

• 0.3333

• 0.6666

• 0.5000

• 0.2500

What is the height of the probability density function for worker 1's task completion time?

• 1/6

• 1/5

• 1/7

• 1/4

What is the range of time for which worker 2's task completion is uniformly distributed?

• 13 to 18 minutes

• 12 to 17 minutes

• 11 to 16 minutes

• 10 to 15 minutes

What fraction represents the probability of worker 2 completing the task between 12 and 15 minutes using the fraction method?

• 2/5

• 3/5

• 4/5

• 1/5

What is the decimal equivalent of the probability that worker 2 completes the task between 12 and 15 minutes?

• 0.7

• 0.4

• 0.5

• 0.6

What is the height of the probability density function for worker 2's task completion time?

• 1/5

• 1/4

• 1/6

• 1/3

What is the base length used to calculate the area for worker 2's task completion probability between 12 and 15 minutes?

• 5

• 2

• 3

• 4