Assignment: 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.
Instructions
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 to 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:
I. Incorrect Answers
Correct any wrong answers. You must also explain the error performed in the problem in your own words.
II. Partially Finished Work
Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.
III. Blank Questions
Show how to complete any blank questions by providing step-by-step instructions including explanations.
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:
1) This problem is an incorrect.Your job is to find the errors, correct the errors, and explain what they did wrong.
2) This problem is partially finished.You must complete the problem by showing all steps while explaining yourself.
3) 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.
I. 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 -1.63 and 1.96
II. 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 65.2 in. and a standard deviation of 3.53in, find the percentage of women that meet the height requirement.
III. Women's pulse rates are normally distributed with a mean of 68.6 beats per minute and a standard deviation of 10.9 beats per minute. What is the z-score for a woman having a pulse rate of 66 beats per minute?
IV. What is the cumulative area from the left under the curve for az-score of -0.785? What is the area on the right of that z-score?
V. If the area under the standard normal distribution curve is 0.6753 from the right, what is the corresponding z-score?
VI. 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 2.9 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?
Format your assignment according to the following formatting requirements:
i) The answer should be typed, using Times New Roman font (size 12), double spaced, with one-inch margins on all sides.
ii) The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
iii) Also include a reference page. The Citations and references must follow APA format. The reference page is not included in the required page length.