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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
6. A hotel manager must distribute salary raises for next year. She has decided that the
- 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb83a8f0d-4687-4289-a4fd-73913ef21dca%2F13ca4d2a-b3a8-4125-88ec-a72baf088199%2Fcxrqdm_processed.png&w=3840&q=75)
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