Assume that Z is a number randomly chosen from a standard normal distribution. Use the standard normal table to calculate each of the following probabilities: a. Pr[Z>1.34] b. Pr[Z<1.34] c. Pr[Z>2.15]
Assume that Z is a number randomly chosen from a standard normal distribution. Use the standard normal table to calculate each of the following probabilities: a. Pr[Z>1.34] b. Pr[Z<1.34] c. Pr[Z>2.15]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Assume that Z is a number randomly chosen from a standard
a. Pr[Z>1.34]
b. Pr[Z<1.34]
c. Pr[Z>2.15]
d. Pr[Z<1.2]
e. Pr[0.52<Z<2.34]
f. Pr[-2.34<Z<-0.52]
g. Pr[Z<-0.93]
h. Pr[Z>-0.93]
i. Pr-1.57<Z<-0.32]
Transcribed Image Text:The image displays a detailed z-table, also known as a standard normal distribution table. This table provides the cumulative probability of a standard normal random variable, typically used in statistics for finding the probability that a statistic is observed below, at, or above a standard score (z-score).
### Table Explanation:
- **Columns and Rows**: The table is organized with z-scores along the rows and additional decimal values in the columns.
- **Z-Scores**:
- The first column on the left represents the whole number and first decimal of the z-score.
- The remaining columns represent the second decimal place of the z-score.
- **Entries**: Each cell within the table shows the probability that a statistic is less than the corresponding z-score. For example, if the z-score is 1.6, the probability is 0.9452.
- **Usage**: To find the cumulative probability of a z-score:
1. Locate the first digit and the first decimal in the row (y-axis).
2. Find the second decimal in the top row (x-axis).
3. The point where the row and column intersect gives the probability.
This table is essential for statistical calculations, especially when working with data that follows a normal distribution pattern. It's commonly used in hypothesis testing, confidence intervals, and other statistical inferences.
Note that the table provided covers z-scores from 1.6 to 4.0, useful for relatively high values, indicating the tail ends of a standard normal distribution.
Transcribed Image Text:The image displays a statistical table used to calculate standard normal distribution probabilities. The heading indicates it applies the formula: `1 - NORM.DIST(1.96, 0, 1, TRUE)`, which relates to the cumulative distribution function for the standard normal distribution.
### Table Breakdown:
- **Rows and Columns**: The table has rows labeled by the first two digits after the decimal (a.bc), ranging from 0.0 to 1.9. The columns, labeled by the second digit after the decimal (c), range from 0 to 9.
- **Purpose**: This table provides probabilities for the standard normal distribution (Z-scores) rounded to two decimal places. For example, if you are looking up a Z-score of 0.45, you first go to the row labeled 0.4 and then move to the column labeled 5. The value at this intersection gives the cumulative probability from the mean.
### Using the Table:
1. **Locate the First Two Digits**: Find the row corresponding to the first two digits of the Z-score.
2. **Find the Second Decimal Place**: Move across the row to the column representing the second decimal place.
3. **Read the Probability**: The cell value is the cumulative probability for that Z-score.
### Example:
- To find the cumulative probability for Z = 0.45:
- Check row 0.4 and then column 5.
- The value is 0.32636.
This table is an essential tool for statistical analysis in fields such as psychology, finance, and any domain requiring normal distribution probabilities. It aids in determining the probability of a value falling below a particular Z-score in a standard normal distribution.
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