Introduction to Probability
Residing in Fort Walton Beach, Florida and working at Eglin AFB. It can be a challenge to drive to each morning since the base is under construction. If there's an accident or construction being worked, this can also increase the wait time it takes me to get to work. Normally it takes a little over 15 minutes before the construction started but now it takes 20 or more minutes. For this SLP, I will be collecting variable data for 10 days on how long it takes me to drive to work each day since it can difficult at times depending on traffic.
- Day 1 - 22 minutes - Construction
- Day 2 - 35 minutes - Construction
- Day 3 - 30 minutes - Construction
- Day 4 - 28 minutes - Construction
- Day 5 - 31 minutes - Construction
- Day 6 - 33 minutes - Construction
- Day 7 - 15 minutes - Normal traffic
- Day 8 - 17 minutes - Normal traffic
- Day 9 - 35 minutes - Accident at intersection
- Day 10 - 18 minutes - Normal
Table 1 showing the sum of the collected wait times. Here, n=10,∑x=264.
The mean waiting time is, x ¯= (∑x)/n= 264/10 = 26.4 minutes
Table 1.
|
Day
|
Wait Time (in min)
|
|
1
|
22
|
|
2
|
35
|
|
3
|
30
|
|
4
|
28
|
|
5
|
31
|
|
6
|
33
|
|
7
|
15
|
|
8
|
17
|
|
9
|
35
|
|
10
|
18
|
|
Sum
|
264
|
Table 2 showing the ordered series (Ascending) of the collected wait times.
Table 2.
|
15
|
17
|
18
|
22
|
28
|
30
|
31
|
33
|
35
|
35
|
Since n=10, is even the mean of the two middle terms is the required median.
The median waiting time is, M= Mean of 5th and 6th terms in the ordered series
= (28 + 30)/2
= 29 minutes
The most frequent value of the collected wait times is 35, i.e. it was repeated 2 times. Therefore, the mode of waiting times is 35 minutes.
Since it was expected that now it takes 20 or more minutesto get to work if there's an accident or construction being worked, the three measures obtained here support the expectations.
Among the calculated 3 measures of central tendency, the mean is the most accurately describes the variable under study. Since the variable wait time is measured on continuous ratio scale, the arithmetic mean is an appropriate measure to describe the central tendency.
Chart 1 contains the box-plot of the collected 10 wait times.
The box-plot depicts that the distribution of wait times is skewed to its left. The values of mean, median and mode (26.4 < 29 < 35) also indicated the same.
Continuing with the data, write a paper (1-3 pages) including all of the following content:
• Include your data from Module 1.
• Create a frequency distribution table for your data. You can use Excelor Word.
• Calculate the standard deviation.
• Calculate the variance.
• Is this a normal distribution? How do you know?
• What are the implications?