Assignment Prompt & Instructions
[>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)
– 2 years ago
**files (4)**
– ## lecture2.pdf
– ## lecture1.pdf
– ## lecture3.pdf
– ## Week5LabTemplate2024.docx
**## lecture2.pdf**
©2024 Chamberlain University 1
MATH225
Empirical Rule (68-95-99.7 Rule)
©2024 Chamberlain University 2
Example:
Example:
©2024 Chamberlain University 3
Example:
Example:
**## lecture1.pdf**
©2024 Chamberlain University 1
MATH225
Parameters of the Normal Distribution
Normal Distributions and Standard Normal Distribution
©2024 Chamberlain University 2
\*\* The more spread out the graph—The greater the standard deviation.
The Standard Normal Distribution
©2024 Chamberlain University 3
Z = 0 -> _________________________________________________________________
Z = negative -> ____________________________________________________________
Z = positive -> ______________________________________________________________
Normal: __________________________________________________________________
Unusual: __________________________________________________________________
Highly Unusual: _____________________________________________________________
Example:
©2024 Chamberlain University 4
Value: _________________________________________________________________
Example: The scores on a test are normally distributed with a mean of 90 and a
standard deviation of 18. What is the score that is 2 ½ standard deviations above
the mean?
Example: The scores on a test are normally distributed with a mean of 130 and a
standard deviation of 26. What is the score that is ½ standard deviation below the
mean?
Example:
©2024 Chamberlain University 5
Example:
Example:
©2024 Chamberlain University 6
Example:
**## lecture3.pdf**
©2024 Chamberlain University 1
MATH225
Normal Distributions to Compute Probability
Finding Areas Under the Standard Normal Curve
1. Sketch the curve and shade the area.
2. Three Cases:
a) To find the area to the left of z, just find the area that
corresponds to z on the table.
Example:
©2024 Chamberlain University 2
b) To find the area to the right of z, just find the area that
corresponds to z on the table and subtract the area from 1.
Example:
c) To find the area between two z-scores find both
corresponding areas and subtract the smaller from the largest.
Example:
Example:
©2024 Chamberlain University 3
Applications of a Normal Distribution
Finding the Probability
Example: The number of miles a motorcycle, X, will travel on one
gallon of gasoline is modeled by a normal distribution with mean 44 and
standard deviation 5.
With one gallon of gasoline in the motorcycle, find the probability that
Mike can travel more than 50 miles without refueling. Round your
answer to four decimal places.
©2024 Chamberlain University 4
Example: A certain type of mango that weights over 450 grams is
considered large in size. The weights for this type of mango, X grams,
are normal distributed with a mean of 400 and a standard deviation of
20.
Find the probability that a randomly selected mango of this type will not
be considered as large size. Round your answer to four decimal places.
Example: A worn, poorly set-up machine is observed to produce
components whose length X follows a normal distribution with a mean
equal to 14 centimeters wand a variance equal to 9.
Determine the probability that a component is at most 12 centimeters
long Round your answer to four decimal places.
Finding the Value given the Probability
©2024 Chamberlain University 5
Recall: To find value– x = mean + z-score*standard deviation
Example: An organization has members who possess IQs in the top 4%
of the population. If IQs are normally distributed, with a mean of 105
and a standard deviation of 15, what is the minimum IQ required for
admission into the organization?
Example: The weights of bags of raisins are normally distributed with a
mean of 175 grams and a standard deviation of 11 grams. Bags in the
upper 4.5% are too heavy and must be repackaged. Also, bags in the
lower 5% do not meet the minimum weight requirement and must be
repackaged.
What are the ranges of weights for raisin bags that need to repackaged.
©2024 Chamberlain University 6
©2024 Chamberlain University 7
**## Week5LabTemplate2024.docx**
**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.
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. 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 | |
| Sample Standard Deviation in inches | |
| Your Height in Inches | |
**1b.** Post a screen shot in the space BELOW of the portion of the 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.**
**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?
**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?
**2.** What part of the country did your study take place in?
**3.** What are the age ranges of your participants?
**4.** How many of each gender did you have in your study?
**5.** What are other interesting factors about your group?
**Step 3. Data Analysis**
Answer the following questions. Use the Week 5 Excel spreadsheets to help analyze the data.
**Empirical Rule**
**1.** Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the 20 heights in your height study. (Use the Empirical Rule tab from the spreadsheet).
**2.** What do these values tell you? Write complete sentences explaining what the values in the Empirical Rule tell you in context of the data.
**3.** Take a Screenshot of your Empirical Rule Sheet (Week 5 Spreadsheet) and provide it below
**Normal Distribution**
1. Take a Screenshot of your Normal Distribution Sheet and provide it below
2. Based on your study results, what percent of the study participants are shorter than you? What percent are taller?
**Step 4. Save and submit this document**
Be sure your name is on the Word document, save it, and then submit it. In the assignment module, click “start assignment” and then “upload file” and “submit assignment”.
| | |
| — | — |
| | 7 |
## image1.jpeg
**## Week5LabTemplate2024.docx**
**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.
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. 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 | |
| Sample Standard Deviation in inches | |
| Your Height in Inches | |
**1b.** Post a screen shot in the space BELOW of the portion of the 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.**
**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?
**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?
**2.** What part of the country did your study take place in?
**3.** What are the age ranges of your participants?
**4.** How many of each gender did you have in your study?
**5.** What are other interesting factors about your group?
**Step 3. Data Analysis**
Answer the following questions. Use the Week 5 Excel spreadsheets to help analyze the data.
**Empirical Rule**
**1.** Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the 20 heights in your height study. (Use the Empirical Rule tab from the spreadsheet).
**2.** What do these values tell you? Write complete sentences explaining what the values in the Empirical Rule tell you in context of the data.
**3.** Take a Screenshot of your Empirical Rule Sheet (Week 5 Spreadsheet) and provide it below
**Normal Distribution**
1. Take a Screenshot of your Normal Distribution Sheet and provide it below
2. Based on your study results, what percent of the study participants are shorter than you? What percent are taller?
**Step 4. Save and submit this document**
Be sure your name is on the Word document, save it, and then submit it. In the assignment module, click “start assignment” and then “upload file” and “submit assignment”.
| | |
| — | — |
| | 7 |
## image1.jpeg
**## lecture2.pdf**
©2024 Chamberlain University 1
MATH225
Empirical Rule (68-95-99.7 Rule)
©2024 Chamberlain University 2
Example:
Example:
©2024 Chamberlain University 3
Example:
Example:
**## lecture1.pdf**
©2024 Chamberlain University 1
MATH225
Parameters of the Normal Distribution
Normal Distributions and Standard Normal Distribution
©2024 Chamberlain University 2
\*\* The more spread out the graph—The greater the standard deviation.
The Standard Normal Distribution
©2024 Chamberlain University 3
Z = 0 -> _________________________________________________________________
Z = negative -> ____________________________________________________________
Z = positive -> ______________________________________________________________
Normal: __________________________________________________________________
Unusual: __________________________________________________________________
Highly Unusual: _____________________________________________________________
Example:
©2024 Chamberlain University 4
Value: _________________________________________________________________
Example: The scores on a test are normally distributed with a mean of 90 and a
standard deviation of 18. What is the score that is 2 ½ standard deviations above
the mean?
Example: The scores on a test are normally distributed with a mean of 130 and a
standard deviation of 26. What is the score that is ½ standard deviation below the
mean?
Example:
©2024 Chamberlain University 5
Example:
Example:
©2024 Chamberlain University 6
Example:
**## lecture3.pdf**
©2024 Chamberlain University 1
MATH225
Normal Distributions to Compute Probability
Finding Areas Under the Standard Normal Curve
1. Sketch the curve and shade the area.
2. Three Cases:
a) To find the area to the left of z, just find the area that
corresponds to z on the table.
Example:
©2024 Chamberlain University 2
b) To find the area to the right of z, just find the area that
corresponds to z on the table and subtract the area from 1.
Example:
c) To find the area between two z-scores find both
corresponding areas and subtract the smaller from the largest.
Example:
Example:
©2024 Chamberlain University 3
Applications of a Normal Distribution
Finding the Probability
Example: The number of miles a motorcycle, X, will travel on one
gallon of gasoline is modeled by a normal distribution with mean 44 and
standard deviation 5.
With one gallon of gasoline in the motorcycle, find the probability that
Mike can travel more than 50 miles without refueling. Round your
answer to four decimal places.
©2024 Chamberlain University 4
Example: A certain type of mango that weights over 450 grams is
considered large in size. The weights for this type of mango, X grams,
are normal distributed with a mean of 400 and a standard deviation of
20.
Find the probability that a randomly selected mango of this type will not
be considered as large size. Round your answer to four decimal places.
Example: A worn, poorly set-up machine is observed to produce
components whose length X follows a normal distribution with a mean
equal to 14 centimeters wand a variance equal to 9.
Determine the probability that a component is at most 12 centimeters
long Round your answer to four decimal places.
Finding the Value given the Probability
©2024 Chamberlain University 5
Recall: To find value– x = mean + z-score*standard deviation
Example: An organization has members who possess IQs in the top 4%
of the population. If IQs are normally distributed, with a mean of 105
and a standard deviation of 15, what is the minimum IQ required for
admission into the organization?
Example: The weights of bags of raisins are normally distributed with a
mean of 175 grams and a standard deviation of 11 grams. Bags in the
upper 4.5% are too heavy and must be repackaged. Also, bags in the
lower 5% do not meet the minimum weight requirement and must be
repackaged.
What are the ranges of weights for raisin bags that need to repackaged.
©2024 Chamberlain University 6
©2024 Chamberlain University 7
**## Week5LabTemplate2024.docx**
**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.
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. 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 | |
| Sample Standard Deviation in inches | |
| Your Height in Inches | |
**1b.** Post a screen shot in the space BELOW of the portion of the 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.**
**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?
**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?
**2.** What part of the country did your study take place in?
**3.** What are the age ranges of your participants?
**4.** How many of each gender did you have in your study?
**5.** What are other interesting factors about your group?
**Step 3. Data Analysis**
Answer the following questions. Use the Week 5 Excel spreadsheets to help analyze the data.
**Empirical Rule**
**1.** Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the 20 heights in your height study. (Use the Empirical Rule tab from the spreadsheet).
**2.** What do these values tell you? Write complete sentences explaining what the values in the Empirical Rule tell you in context of the data.
**3.** Take a Screenshot of your Empirical Rule Sheet (Week 5 Spreadsheet) and provide it below
**Normal Distribution**
1. Take a Screenshot of your Normal Distribution Sheet and provide it below
2. Based on your study results, what percent of the study participants are shorter than you? What percent are taller?
**Step 4. Save and submit this document**
Be sure your name is on the Word document, save it, and then submit it. In the assignment module, click “start assignment” and then “upload file” and “submit assignment”.
| | |
| — | — |
| | 7 |
## image1.jpeg
**## lecture2.pdf**
©2024 Chamberlain University 1
MATH225
Empirical Rule (68-95-99.7 Rule)
©2024 Chamberlain University 2
Example:
Example:
©2024 Chamberlain University 3
Example:
Example:
**## lecture1.pdf**
©2024 Chamberlain University 1
MATH225
Parameters of the Normal Distribution
Normal Distributions and Standard Normal Distribution
©2024 Chamberlain University 2
\*\* The more spread out the graph—The greater the standard deviation.
The Standard Normal Distribution
©2024 Chamberlain University 3
Z = 0 -> _________________________________________________________________
Z = negative -> ____________________________________________________________
Z = positive -> ______________________________________________________________
Normal: __________________________________________________________________
Unusual: __________________________________________________________________
Highly Unusual: _____________________________________________________________
Example:
©2024 Chamberlain University 4
Value: _________________________________________________________________
Example: The scores on a test are normally distributed with a mean of 90 and a
standard deviation of 18. What is the score that is 2 ½ standard deviations above
the mean?
Example: The scores on a test are normally distributed with a mean of 130 and a
standard deviation of 26. What is the score that is ½ standard deviation below the
mean?
Example:
©2024 Chamberlain University 5
Example:
Example:
©2024 Chamberlain University 6
Example:
**## lecture3.pdf**
©2024 Chamberlain University 1
MATH225
Normal Distributions to Compute Probability
Finding Areas Under the Standard Normal Curve
1. Sketch the curve and shade the area.
2. Three Cases:
a) To find the area to the left of z, just find the area that
corresponds to z on the table.
Example:
©2024 Chamberlain University 2
b) To find the area to the right of z, just find the area that
corresponds to z on the table and subtract the area from 1.
Example:
c) To find the area between two z-scores find both
corresponding areas and subtract the smaller from the largest.
Example:
Example:
©2024 Chamberlain University 3
Applications of a Normal Distribution
Finding the Probability
Example: The number of miles a motorcycle, X, will travel on one
gallon of gasoline is modeled by a normal distribution with mean 44 and
standard deviation 5.
With one gallon of gasoline in the motorcycle, find the probability that
Mike can travel more than 50 miles without refueling. Round your
answer to four decimal places.
©2024 Chamberlain University 4
Example: A certain type of mango that weights over 450 grams is
considered large in size. The weights for this type of mango, X grams,
are normal distributed with a mean of 400 and a standard deviation of
20.
Find the probability that a randomly selected mango of this type will not
be considered as large size. Round your answer to four decimal places.
Example: A worn, poorly set-up machine is observed to produce
components whose length X follows a normal distribution with a mean
equal to 14 centimeters wand a variance equal to 9.
Determine the probability that a component is at most 12 centimeters
long Round your answer to four decimal places.
Finding the Value given the Probability
©2024 Chamberlain University 5
Recall: To find value– x = mean + z-score*standard deviation
Example: An organization has members who possess IQs in the top 4%
of the population. If IQs are normally distributed, with a mean of 105
and a standard deviation of 15, what is the minimum IQ required for
admission into the organization?
Example: The weights of bags of raisins are normally distributed with a
mean of 175 grams and a standard deviation of 11 grams. Bags in the
upper 4.5% are too heavy and must be repackaged. Also, bags in the
lower 5% do not meet the minimum weight requirement and must be
repackaged.
What are the ranges of weights for raisin bags that need to repackaged.
©2024 Chamberlain University 6
©2024 Chamberlain University 7
**## Week5LabTemplate2024.docx**
**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.
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. 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 | |
| Sample Standard Deviation in inches | |
| Your Height in Inches | |
**1b.** Post a screen shot in the space BELOW of the portion of the 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.**
**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?
**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?
**2.** What part of the country did your study take place in?
**3.** What are the age ranges of your participants?
**4.** How many of each gender did you have in your study?
**5.** What are other interesting factors about your group?
**Step 3. Data Analysis**
Answer the following questions. Use the Week 5 Excel spreadsheets to help analyze the data.
**Empirical Rule**
**1.** Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the 20 heights in your height study. (Use the Empirical Rule tab from the spreadsheet).
**2.** What do these values tell you? Write complete sentences explaining what the values in the Empirical Rule tell you in context of the data.
**3.** Take a Screenshot of your Empirical Rule Sheet (Week 5 Spreadsheet) and provide it below
**Normal Distribution**
1. Take a Screenshot of your Normal Distribution Sheet and provide it below
2. Based on your study results, what percent of the study participants are shorter than you? What percent are taller?
**Step 4. Save and submit this document**
Be sure your name is on the Word document, save it, and then submit it. In the assignment module, click “start assignment” and then “upload file” and “submit assignment”.
| | |
| — | — |
| | 7 |
## image1.jpeg