The area between z = 0 and z = 2.55 is %3D %3D

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
Topic Video
Question
100%

I need help understanding how to get the answer on this problem. Thank you!

### Finding the Area Under the Standard Normal Curve

**Objective**: Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

**Problem**:
Calculate the area between \( z = 0 \) and \( z = 2.55 \).

\[ \text{The area between } z = 0 \text{ and } z = 2.55 \text{ is } \_\_\_\_. \]

**Instructions**:
1. **Sketch the Standard Normal Curve**:
    - Draw a standard normal curve (bell-shaped curve).
    - Label the horizontal axis with z-scores.
    - Mark \( z = 0 \) at the mean (center of the curve).
    - Mark \( z = 2.55 \) on the right side of the mean.

2. **Shaded Area**:
    - Shade the area under the curve between \( z = 0 \) and \( z = 2.55 \).

3. **Finding the Area**:
    - Use standard normal distribution tables or software tools to find the cumulative area from \( z = 0 \) to \( z = 2.55 \).

4. **Round the Answer**:
    - Round the computed area to four decimal places and fill in the blank.

**Steps to Calculate the Area**:
1. Look up the cumulative area from the z-table for \( z = 2.55 \). 
2. The cumulative area to the left of \( z = 2.55 \) is typically found in the table.
3. Since the area under the curve from \( z = 0 \) to \( z = 2.55 \) is needed, subtract the cumulative area up to \( z = 0 \) (which is 0.5) from the cumulative area up to \( z = 2.55 \).
4. The resulting value is the area between \( z = 0 \) and \( z = 2.55 \).

This exercise will help in understanding how to use the standard normal distribution table and graphically represent areas under the curve for specified z-score intervals.
Transcribed Image Text:### Finding the Area Under the Standard Normal Curve **Objective**: Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) **Problem**: Calculate the area between \( z = 0 \) and \( z = 2.55 \). \[ \text{The area between } z = 0 \text{ and } z = 2.55 \text{ is } \_\_\_\_. \] **Instructions**: 1. **Sketch the Standard Normal Curve**: - Draw a standard normal curve (bell-shaped curve). - Label the horizontal axis with z-scores. - Mark \( z = 0 \) at the mean (center of the curve). - Mark \( z = 2.55 \) on the right side of the mean. 2. **Shaded Area**: - Shade the area under the curve between \( z = 0 \) and \( z = 2.55 \). 3. **Finding the Area**: - Use standard normal distribution tables or software tools to find the cumulative area from \( z = 0 \) to \( z = 2.55 \). 4. **Round the Answer**: - Round the computed area to four decimal places and fill in the blank. **Steps to Calculate the Area**: 1. Look up the cumulative area from the z-table for \( z = 2.55 \). 2. The cumulative area to the left of \( z = 2.55 \) is typically found in the table. 3. Since the area under the curve from \( z = 0 \) to \( z = 2.55 \) is needed, subtract the cumulative area up to \( z = 0 \) (which is 0.5) from the cumulative area up to \( z = 2.55 \). 4. The resulting value is the area between \( z = 0 \) and \( z = 2.55 \). This exercise will help in understanding how to use the standard normal distribution table and graphically represent areas under the curve for specified z-score intervals.
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
Data Collection, Sampling Methods, and Bias
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.
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