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# Week 5 Math Lab Assignment (Math Problem Sample)

Instructions:

This paper documents a Week 5 Lab Assignment for MATH225, focusing on analyzing height data using statistical tools such as mean, standard deviation, and the Empirical Rule. The assignment begins by collecting two sets of height data: one set provided by the instructor and another collected by the student through random sampling. The combined data forms a sample of 20 heights, with the mean height calculated as 65.1 inches and the standard deviation as 3.51 inches. The student's height (69 inches) is slightly taller than the sample mean.
The assignment further examines data characteristics by identifying the sampling method, which was simple random sampling, and detailing the demographics of the participants, who were football players from Illinois aged 23 to 28. The gender distribution included six males and four females, representing a small population of football players in Illinois.
The data analysis section applies the Empirical Rule to determine the ranges for 68%, 95%, and 99.7% of the data distribution. The findings show that 68% of the data falls between 61.59 and 68.61 inches, while 95% lies between 58.08 and 72.12 inches, and 99.7% is within 54.58 to 75.62 inches. These values illustrate the spread of the height data around the mean.
The assignment also calculates the probability that an individual from the sample is shorter or taller than the student. It reveals that 27.47% of the population is shorter than the student, while 8.12% are taller. The use of statistical tools such as the Z-score and normal probability spreadsheet aids in these calculations, providing a comprehensive analysis of height distribution within the sample. source..

Content:

MATH225
Week 5 Lab Assignment
Name:________________________ Instructor Name: _______________
Please use this template to help answer the questions listed in the lab instructions. The “steps” below refer to the steps listed in the lab instructions. Type your answers and post your screenshots in the spaces given below. Then, save this document with your name and submit it inside the course room.
Step 1. Gather Data
Your instructors will post 10 data values to use for this lab. The data values represent the HEIGHTS of 10 people from the same population in which you gathered your sample.
Please reach out to your instructor if you did not receive the assigned 10 data values for the term by Monday of Week 5.
(NOTE: This is NOT the data used in the lab video, which is about midterm grades. Do not use the midterm grades data.)
1a. Gather 10 MORE of your own to add to the 10 provided by your instructor. Do the following: Survey or measure 10 people to find their heights. For the remainder of this lab, treat the 20 numbers as ONE sample.
Instructor Provided Heights
62
62
62
63
65
67
68
69
69
73
Gathered Heights
60
61
61
63
64
64
66
66
67
70
Determine the mean and standard deviation for the 20 values by using the Week 3 Excel spreadsheet. (Round statistics to two decimals.)
Mean Height in Inches
65.1000
Sample Standard Deviation in inches
3.5079
Your Height in Inches
69
1b. Post a screen shot in the space BELOW of the portion of the Week 3 spreadsheet that helped you determine these values. Please list the 10 heights your professor provided first followed by the 10 heights you collected. There should be 20 values to determine the mean and sample standard deviation.
Data
62
62
62
63
65
67
68
69
69
73
60
61
61
63
64
64
66
66
67
70
1c. Answer the following two questions (Answer in complete sentences).
How does your height compare to the mean (average) height of the 20 values? Is your height taller, shorter, or the same as the mean of the sample?
My height is 69 inches, which is slightly taller than the average mean of 65.1 in the sample population. This variation indicates that most of the participants chosen for the sampling ranged between 64 and 66 percent of the total population.
Step 2. Data Characteristics
Answer the following questions to give some background information on the group of people you used in your study. Write in complete sentences.
1. How did you choose the participants for your study? What was the sampling method: systematic, convenience, cluster, stratified, simple random, etc.? Explain how you concluded that you used the selected sampling method.
Most of the time, I usually go for football exercises at the Westside Stadium near my residence. Last weekend, I did a simple random method by gathering our team players and requested I use their heights for the Math lab assignment. I proceeded with data collection using simple random sampling, and I randomly selected 10 of the football players out of the population. In this sampling technique, each member of the total population has an accurately equal chance of being selected.
2. What part of the country did your study take place in?
Illinois State
3. What are the age ranges of your participants?
23-28 Years
4. How many of each gender did you have in your study?
6 – Males
4 – Females
5. Identify the population based on the sample gathered. For example, if you sampled people that worked on your floor in the hospital, your population may be all employees at your hospital or if you sampled your neighbors, maybe the population is everyone who lives in your city.
Football players who live in Illinois States
Step 3. Data Analysis
Answer the following questions. Use the Week 5 Excel spreadsheets to help analyze the data.
For the remainder of the lab, suppose the population has the same mean and standard deviation as your sample.
Empirical Rule
1. Determine the 68%, 95%, and 99.7% values of the Empirical Rule using the population mean and standard deviation. (Use the Empirical Rule tab from the Week 5 spreadsheet).
1 68% values of Empirical Rule: 61.5291
2 95% values of Empirical Rule: 58.0842
3 99% values of Empirical Rule: 54.5763
2. Take a Screenshot of your Empirical Rule Sheet and provide it below.
ANSWER
Empirical Rule
68-95-99.7
mean
65.1
Lower number
Upper number
standard deviation
3.5079
68%
61.5921
68.61
95%
58.0842
72.12
99.70%
54.5763
...

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