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07.02.2025
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lecture2.pdf

lecture1.pdf

lecture3.pdf

Week5LabTemplate2024.docx

lecture2.pdf

MATH225 Empirical Rule (68-95-99.7 Rule)

Example:

lecture1.pdf

MATH225 Parameters of the Normal Distribution

Normal Distributions and Standard Normal Distribution

** The more spread out the graph—The greater the standard deviation.

The Standard Normal Distribution

Z = 0 -> _________________________________________________________________ Z = negative -> ____________________________________________________________ Z = positive -> ______________________________________________________________ Normal: __________________________________________________________________ Unusual: __________________________________________________________________ Highly Unusual: _____________________________________________________________ Example:

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:

Example:

lecture3.pdf

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:

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:

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.

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

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.

Week5LabTemplate2024.docx

C:\Users\D01030541\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Outlook\7T7OKQBI\Pre-licensure Header_Seal Only (3).jpg

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”.

image1.jpeg

lecture2.pdf

MATH225 Empirical Rule (68-95-99.7 Rule)

Example:

lecture1.pdf

MATH225 Parameters of the Normal Distribution

Normal Distributions and Standard Normal Distribution

** The more spread out the graph—The greater the standard deviation.

The Standard Normal Distribution

Example:

lecture3.pdf

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:

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:

Applications of a Normal Distribution

Week5LabTemplate2024.docx

C:\Users\D01030541\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Outlook\7T7OKQBI\Pre-licensure Header_Seal Only (3).jpg

Week 5 Lab Assignment

Name:________________________ Instructor Name: _______________

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.)

Mean Height in Inches
Sample Standard Deviation in inches
Your Height in Inches

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”.

image1.jpeg

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