Public Transportation

The mayor and city council members of Seatville have hired you as a consultant to determine the transportation modes within their city. The mayor wants to know where to spend budget dollars to improve infrastructure and transportation modes. Being a diligent consultant, you interviewed 1,255 people during a 16-week period. You determined the following methods of transportation were used:

· 850 residents drove a personal car,

· 200 used public transportation (bus),

· 5 rode a bicycle,

· 50 walked, and

· 150 rode a motorcycle.

Prepare homework that outlines the requirements of your consulting task. In your homework, you should include the following:

1. Provide an introduction that outlines the problem and gives on overview of the situation as well as a conclusion that sums up your homework.

2. Develop and explain the probability and relative frequency of the data you found for each mode of transportation.

3. Compute the relative frequencies to two decimal places

4. Use this data to make a final recommendation of where the mayor and city council should spend their infrastructure/transportation.

Your completed homework must be at least three pages, and you must use your textbook and at least one other academic source. Adhere to APA Style when constructing this assignment, including in-text citations and references for all sources that are used. Please note that no abstract is needed.

Class Text Book

Render, Barry, et al. Quantitative Analysis for Management. Available from: VitalSource Bookshelf, (13th Edition). Pearson Education (US), 2017.

Pg. From textbook to use in report.

Probability Distribution of a Discrete Random Variable When we have a discrete random variable, there is a probability value assigned to each event. These values must be between 0 and 1, and they must sum to 1. Let’s look at an example. The 100 students in Pat Shannon’s statistics class have just completed a math quiz that he gives

on the first day of class. The quiz consists of five very difficult algebra problems. The grade on the quiz is the number of correct answers, so the grades theoretically could range from 0 to 5. However, no one in this class received a score of 0, so the grades ranged from 1 to 5. The random variable X is defined to be the grade on this quiz, and the grades are summarized in Table 2.7. This discrete prob-ability distribution was developed using the relative frequency approach presented earlier. The distribution follows the three rules required of all probability distributions: (1) the

events are mutually exclusive and collectively exhaustive, (2) the individual probability values are between 0 and 1 inclusive, and (3) the total of the probability values is 1. Although listing the probability distribution as we did in Table 2.7 is adequate, it can be

difficult to get an idea about characteristics of the distribution. To overcome this problem, the probability values are often presented in graph form. The graph of the distribution in Table 2.7 is shown in Figure 2.4. The graph of this probability distribution gives us a picture of its shape. It helps us identify the central tendency of the distribution, called the mean or expected value, and the amount of variability or spread of the distribution, called the variance.

The expected value of a discrete distribution is the weighted average of the values of the random variable.

Expected Value of a Discrete Probability Distribution Once we have established a probability distribution, the first characteristic that is usually of interest is the central tendency of the distribution. The expected value, a measure of central ten-dency, is computed as the weighted average of the values of the random variable: