A hotel manager must distribute salary raises for next year.  She has decided that the mean raise is to be $2,000, the standard deviation of the raise is to be $400, and the distribution approximates normally.   the highest 10% of the employees (ranked by merit) will have a raise equal to or greater than $___________. b.  the 5% of the employees with the lowest merit rating will receive no more  than $__________ each.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%

6.  A hotel manager must distribute salary raises for next year.  She has decided that the mean raise is to be $2,000, the standard deviation of the raise is to be $400, and the distribution approximates normally.

 

  1. the highest 10% of the employees (ranked by merit) will have a raise equal to or greater than $___________.

b.  the 5% of the employees with the lowest merit rating will receive no more  than $__________ each.

This image presents a Z-table, a statistical table used to find the probability of a standard normal distribution below a particular z-score. The table consists of values representing the cumulative probability from the mean (z = 0) to a given z-score. Each cell shows the probability associated with a particular z-score.

### How to Read the Table:

- **Rows and Columns:** The leftmost column labels the z-score up to the tenths place, and the topmost row labels present the z-score to the hundredths place. To find the cumulative probability for a z-score, combine a row and a column.

- **Example:**
  - For a z-score of 0.57, locate the row for 0.5 and the column for 0.07. The intersection point, 0.7157, shows the probability that a random variable is within 0.57 standard deviations above the mean.

### Detailed Explanation:

1. **Z-Score Range:**
   - The table ranges from z = 0.00 to z = 3.00, covering both the negative and positive sides of the standard normal distribution curve.
   
2. **Interpretation:** 
   - The values indicate the area under the normal curve to the left of the z-score. In other words, it shows the probability that a score will fall between the mean and the given z-score.

This tool is essential for calculating probabilities in statistics, particularly useful in hypothesis testing and confidence interval estimation.
Transcribed Image Text:This image presents a Z-table, a statistical table used to find the probability of a standard normal distribution below a particular z-score. The table consists of values representing the cumulative probability from the mean (z = 0) to a given z-score. Each cell shows the probability associated with a particular z-score. ### How to Read the Table: - **Rows and Columns:** The leftmost column labels the z-score up to the tenths place, and the topmost row labels present the z-score to the hundredths place. To find the cumulative probability for a z-score, combine a row and a column. - **Example:** - For a z-score of 0.57, locate the row for 0.5 and the column for 0.07. The intersection point, 0.7157, shows the probability that a random variable is within 0.57 standard deviations above the mean. ### Detailed Explanation: 1. **Z-Score Range:** - The table ranges from z = 0.00 to z = 3.00, covering both the negative and positive sides of the standard normal distribution curve. 2. **Interpretation:** - The values indicate the area under the normal curve to the left of the z-score. In other words, it shows the probability that a score will fall between the mean and the given z-score. This tool is essential for calculating probabilities in statistics, particularly useful in hypothesis testing and confidence interval estimation.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman