Explain to the parent what this score means

Assignment Help Management Theories

Reference no: EM133767989

Case: About the Assignment: This discussion you'll be given the option of selecting two of three scenarios to write about. Each scenario asks you to apply concepts from the normal distribution, z-scores, and the standard normal distribution. Let's get started!

Directions:

In total your original post will will be 300 to 400 words. It will include the following:

1 to 2 paragraphs on:

in your own words, what is the normal distribution? What are it's major properties?
in your own words, what is a z-score, provide at least two of their characteristics or examples of their use in statistics
1 to 2 paragraphs per scenario.

Answering questions from two scenarios provided (100 words minimum, elaborate thoroughly)
Note: There are no calculations need for these scenarios, simply interpretation of the numbers
Scenario 1

A parent takes their child to a speech pathologist who let's them know that they have scored -1.2z below the mean. In your essay include the answer to these questions:

a. Explain to the parent what this score means in detail especially in relation to the mean and standard deviation.

b. Should the parent be concerned that their child is scoring below -1z, why or why not?

c. After much practice the child is now scoring -.09z, is this a big improvement? Where are they now in relation to the mean?

Scenario 2

A school district is evaluating the performance of students on standardized tests across different schools. Here are the results of two schools.

Woodbury Elementary = +.98Z

Huerta Elementary = -1.95Z

In your essay answer the following questions:

a. Based on a z of +.98z, how many standard deviations higher is Woodbury Elementary scoring above the average? How much so in relation to everyone else, consider using the 68-95-99.7 rule (the standard normal distribution) to explain your answer.

b. Another school (Huerta Elementary) is scoring Z = -1.95z. Explain this score, and compare and contrast their z-score with Woodbury Elementary's z-score in relation to the 68-95-99.7 rule (the standard normal distribution)

Scenario 3

A financial institution is evaluating the creditworthiness of loan applicants. They want to determine whether an applicant's financial data, such as income and credit score, falls within acceptable risk levels. Below are the z-scores of 8 applicants. In this scenario, Z = 0 indicates average risk, negative Zs indicate below average risk, and positive Zs represent above average risk.

Applicant's Z-score:

-1.2z, -1.0z, -.45z, -.22z, -.11z, +0.15z, +1.10z, 1.25z

In your essay include the answer to these questions:

a. Which applicants should they accept? Which applicants should they not accept? Explain your answer based on what you know about z-scores.

b. They ask you to come up with the maximum z-score someone should have in order to be accepted for a loan. If Z = 0 is considered average risk, what z-score would you say should serve as the limit for amount of risk the institution should take? Why this z-score, explain your reasoning.

Reference no: EM133767989

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