Homework answers / question archive / Deliverable 2 - Tutoring on the Normal Distribution Competency Demonstrate the use of the normal distribution, the standard normal distribution, and the central limit theorem for calculating areas under the normal curve and exploring these concepts in real life applications

Deliverable 2 - Tutoring on the Normal Distribution Competency Demonstrate the use of the normal distribution, the standard normal distribution, and the central limit theorem for calculating areas under the normal curve and exploring these concepts in real life applications

Statistics

Share With

---

Deliverable 2 - Tutoring on the Normal Distribution

Competency
Demonstrate the use of the normal distribution, the standard
normal distribution, and the central limit theorem for calculating
areas under the normal curve and exploring these concepts in real
life applications.
Scenario
Frank has only had a brief introduction to statistics when he was in
high school 12 years ago, and that did not cover inferential
statistics. He is not confident in his ability fo answer some of the
problems posed in the course.
As Frank's tutor, you need to provide Frank with guidance and
instruction on a worksheet he has partially filled out. Your job is to
help him understand and comprehend the material. You should
not simply be providing him with an answer as this will not help
when it comes time to take the test. Instead, you will be providing
a step-by-step breakdown of the problems including an
explanation on why you did each step and using proper
terminology.

What to Submit
To complete this assignment, you must first download the word
document
, and then complete it by including the following items on the
worksheet:
1. Incorrect Answers
¢ Correct any wrong answers. You must also explain the error
performed in the problem in your own words.
¢« Partially Finished Work
e Complete any partially completed work. Make sure
to provide step-by-step instructions including
explanations.
¢« Blank Questions
e Show how to complete any blank questions by
providing step-by-step instructions including
explanations,
Your step-by-step breakdown of the problems, including
explanations, should be present within the word document
provided. You must also include an Excel workbook which shows

Not No Pass Competence | Proficiency | Mastery
Submitted

Not Did not Correctly solved a j Correctly solved All problems
Submitted | correctly solve majority of the | almost all the are solved
| a majority of problems. | — problems. correctly.
| the problems
or at least one
problem left :
blank. :
Not | Very few Fairly complete and Mostly complete Complete and
| Submitted | steps are detailed steps are and detailed detailed steps
provided to provided to explain steps are are provided |
| explain how how to solve the providedto | toexplain |
| | to solve the problem OR the explain how to how to solve
problem OR steps provided have | _ solve the the problem. :
the steps some errors. problem. |
provided have
: several |
errors.
Not Explanations Explanations Explanations : Explanations
Submitted aenerallv lack demonstrate a hasic demonstrate a . demonstrate

Deliverable 02 – Worksheet
 

Instructions:  The following worksheet is shown to you by a student who is asking for help. Your job is to help the student walk through the problems by showing the student how to solve each problem in detail. You are expected to explain all of the steps in your own words.

Key:

• <i> - This problem is an incorrect. Your job is to find the errors, correct the errors, and explain what they did wrong.
• <p> - This problem is partially finished. You must complete the problem by showing all steps while explaining yourself.
• <b> - This problem is blank. You must start from scratch and explain how you will approach the problem, how you solve it, and explain why you took each step.

 

1. <p> Assume that a randomly selected subject is given a bone density test. Those tests follow a standard normal distribution. Find the probability that the bone density score for this subject is between -1.53 and 1.98

 

Student’s answer: We first need to find the probability for each of these z-scores using Excel.

For -1.53 the probability from the left is 0.0630, and for 1.98 the probability from the left is 0.9761.

 

Continue the solution:

 

Finish the problem giving step-by-step instructions and explanations.

 

 

 

 

 

2. <b> The U.S. Airforce requires that pilots have a height between 64 in. and 77 in. If women’s heights are normally distributed with a mean of 65 in. and a standard deviation of 3.5 in, find the percentage of women that meet the height requirement.

           

Answer and Explanation:

 

Enter your step-by-step answer and explanations here.

 

 

 

 

3. <i> Women’s pulse rates are normally distributed with a mean of 69.4 beats per minute and a standard deviation of 11.3 beats per minute. What is the z-score for a woman having a pulse rate of 66 beats per minute?

 

Student’s answer:

Let z =x-μσ

 
 

 

z =69.4 - 6611.3

 

 

z = 0.03

 

 

            Corrections:

 

Enter your corrections and explanations here.

 

4. <b> What is the cumulative area from the left under the curve for a z-score of -0.875? What is the area on the right of that z-score?

           

Answer and Explanation:

 

Enter your step-by-step answer and explanations here.

 

 

 

5. <i> If the area under the standard normal distribution curve is 0.6573 from the right, what is the corresponding z-score?

 

Student’s answer: We plug in “=NORM.INV(0.6573, 0, 1)” into Excel and get a z-score of 0.41.

 

Corrections:

 

Enter your corrections and explanations here.

 

 

 

 

6. <p> Manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. Men have shoulder widths that are normally distributed with a mean of 18.2 and a standard deviation of 2.09 in. Assume that a manhole cover is constructed with a diameter of 22.5 in. What percentage of men will fit into a manhole with this diameter?

 

Student’s answer: We need to find the probability that men will fit into the manhole. The first step is to find the probability that the men’s shoulder is less than 22.5 inches.

 

Continue the solution:

Enter your step-by-step answer and explanations here.