Question

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is

Answer 1

20 %

Explanation:

This question can be easily solved using The Rectangular, or Uniform Distribution of Probability

The probability of people arriving between 8:40 am and 9:30 am is uniformly distributed and can be represented by a rectangle attached as figure 1 .

The total area of this green rectangle must be equal to 1 because the total probability is always equal to 1.

We are interested in finding the red region which is for the time range of 9:00 am to 9:10am shown in the figure 2 attached:

First we need to find the Height of this rectangle:

To find the value of Height:

The formula for the area of rectangle = Base x Height

Base = b – a

In our case b – a is the difference in time from 8:40 am to 9:30 am

So, b – a = 50 (mins)

Similarly, Height x Base = 1 because max probability is equal to 1

Height = 1/ (b – a) because Base x Height must be equal to 1 (max probability)

Height = 1/ (b – a )

Height = 1/(Base)

Height = 1/50

Now once we have the value of Height we can find the desired probability of any region by multiplying the Height with the given time range in the question. In our case the time range is 9:00 am to 9:10 am which means 10(mins). Therefore,

Probability = Height x 10

Probability = 1/50 x 10

Probability = 1/5

To convert it into percentage

1/5 x 100% = 20% (Answer)