Mat201 Mod 3 Case

Module 3 - Case

Normal and Standard Distributions

Assignment Overview

To complete this assignment, first review Chapter 6: The Normal Distribution from the background reading using the OpenStax e-textbook. Please have special focus on the following sections:

6.1 The Standard Normal Distribution 6.2 Using the Normal Distribution 6.3 Normal Distribution- Lap Times 6.4 Normal Distribution- Pinkie Length

By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

Case Assignment

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

1. The average score of a statistics class was 71 with a standard deviation of 10.
   1. What is the z score of a student with a grade of 68? (2.5 pts)
   2. What is the z score of a student with a grade of 80? (2.5 pts)
2. Using the same data in #1 answer the following:
   1. Approximately 68% (one standard deviation) of the scores are between ________ and _________ (2.5 pts)
   2. Approximately 95% (two standard deviation) of the scores are between _________ and _________ (2.5 pts)
3. Most values of a standard normal distribution are between __________. (3 pts)
   1. -3 and 3
   2. 0 and 1
   3. 0 and 3
   4. 1 and 3
4. (a) If the standard deviation of a data set is 1.3, what is the variance? (2.5 pts)
   (b) If the variance is 36, what is the standard deviation? (2.5 pts)
5. Let X have a normal distribution with mean µ = 20 and standard deviation σ = 4.
   Determine the area in the normal curve for which:
   1. P(X > 28) (2.5 pts)
   2. P(X < 12) (2.5 pts)
   3. P(16 < X < 24) (2.5 pts)
6. The IQ scores of students listed below are from a SAMPLE of MATH 300 class.

   IQ Scores	92	110	105	96	120	100	90	98	110	95
   	102	99	93	119	106	103	91	101	97	105

   1. What is the mean IQ score? Round to the nearest whole number. (2.5 pts)
   2. Compute the IQ scores within plus/minus one standard deviation? Two answers. Round to the nearest whole numbers. (2.5 pts)
   3. Compute the IQ scores within plus/minus two standard deviation? Two answers. (2.5 pts)
7. Let X have a normal distribution with µ= 10 and standard deviation σ= 2. Transform X to the standard normal form Z and match the following probability statements:
   
   a) P(X>14) 1) P(Z<-1)
   b) P(X<8) 2) P(-2 < Z < 2)
   c) P(6 < X < 14) 3) P(Z > 2)
   
   a) is matched to ___________ (2.5 pts)
   
   b) is matched to ___________ (2.5 pts)
   
   c) is matched to ___________ (2.5 pts)
8. Let X have a normal distribution with mean µ= 30 and standard deviation σ= 10. Calculate P(X>40). Round to two decimal places. (4 pts)
9. For a standard normal variable Z, compute P(Z<1.5). Round your answer to two decimal places. (3 pts)
10. A larger standard deviation of a normal distribution indicates that the distribution becomes (2.5 pts)
    1. narrower and more peaked
    2. flatter and wider
    3. more skewed to the right
    4. more skewed to the left