MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -1.99 and -0.67 and draw a sketch of the region.

**Sketch the region. Choose the correct graph below.**

**Options:**

- **A.** A normal distribution curve with the region between -1.99 and -0.67 shaded on the left side of the mean.
- **B.** A normal distribution curve with the region between -1.99 and -0.67 shaded on both sides of the mean.
- **C.** A normal distribution curve with the region between -1.99 and -0.67 shaded on the right side of the mean.

The probability is [ ].  
(Round to four decimal places as needed.)

*Click to select your answer(s).*

(Note: In option C, the shaded region correctly highlights the area between -1.99 and -0.67 on the left side of the mean on the normal distribution curve, indicating the probability of this range.)
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Transcribed Image Text:Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between -1.99 and -0.67 and draw a sketch of the region. **Sketch the region. Choose the correct graph below.** **Options:** - **A.** A normal distribution curve with the region between -1.99 and -0.67 shaded on the left side of the mean. - **B.** A normal distribution curve with the region between -1.99 and -0.67 shaded on both sides of the mean. - **C.** A normal distribution curve with the region between -1.99 and -0.67 shaded on the right side of the mean. The probability is [ ]. (Round to four decimal places as needed.) *Click to select your answer(s).* (Note: In option C, the shaded region correctly highlights the area between -1.99 and -0.67 on the left side of the mean on the normal distribution curve, indicating the probability of this range.)
The image shows a laptop screen displaying two pages of a Standard Normal Table, commonly used in statistics to find the probabilities associated with a standard normal distribution (Z-scores).

### **Standard Normal Table (Page 1):**

- **Z-Score Values:** Range from -1.6 to 0.0, with increments of 0.1.
- **Probability Values:** Displayed as four-digit numbers representing cumulative probabilities for each Z-score.
- **Table Layout:** The leftmost column represents the Z-score, and the subsequent columns correspond to the second decimal place of the Z-score.
- **Example Entry:** For a Z-score of -1.6 and 0.05, the cumulative probability is 0.0548.
- **Note:** For Z-scores below -3.49, use an area of 0.0001.
- **Interpolation Example:**  
  - Z = -1.645, Area = 0.0500  
  - Z = -2.575, Area = 0.0050

### **Standard Normal Table (Page 2):**

- **Z-Score Values:** Range from 2.0 to 3.4, with increments of 0.1.
- **Probability Values:** Displayed as four-digit numbers similar to page 1.
- **Layout:** The format mirrors page 1, with Z-scores in the leftmost column.
- **Example Entry:** For a Z-score of 2.0 and 0.03, the cumulative probability is 0.9778.
- **Note:** For Z-scores above 3.49, use an area of 0.9999.
- **Interpolation Example:**  
  - Z = 1.645, Area = 0.9500  
  - Z = 2.575, Area = 0.9950

### **Common Critical Values Table:**

- **Confidence Level 90%:** Critical Z = 1.645
- **Confidence Level 95%:** Critical Z = 1.960
- **Confidence Level 99%:** Critical Z = 2.576

### **Additional Notes:**

- The tables provide a quick reference to find probabilities and Z-scores without the need for calculation.
- “Print” and “Done” buttons are visible, indicating options for output or closure of the screen.

This setup aids in the understanding of how Z-scores relate
expand button
Transcribed Image Text:The image shows a laptop screen displaying two pages of a Standard Normal Table, commonly used in statistics to find the probabilities associated with a standard normal distribution (Z-scores). ### **Standard Normal Table (Page 1):** - **Z-Score Values:** Range from -1.6 to 0.0, with increments of 0.1. - **Probability Values:** Displayed as four-digit numbers representing cumulative probabilities for each Z-score. - **Table Layout:** The leftmost column represents the Z-score, and the subsequent columns correspond to the second decimal place of the Z-score. - **Example Entry:** For a Z-score of -1.6 and 0.05, the cumulative probability is 0.0548. - **Note:** For Z-scores below -3.49, use an area of 0.0001. - **Interpolation Example:** - Z = -1.645, Area = 0.0500 - Z = -2.575, Area = 0.0050 ### **Standard Normal Table (Page 2):** - **Z-Score Values:** Range from 2.0 to 3.4, with increments of 0.1. - **Probability Values:** Displayed as four-digit numbers similar to page 1. - **Layout:** The format mirrors page 1, with Z-scores in the leftmost column. - **Example Entry:** For a Z-score of 2.0 and 0.03, the cumulative probability is 0.9778. - **Note:** For Z-scores above 3.49, use an area of 0.9999. - **Interpolation Example:** - Z = 1.645, Area = 0.9500 - Z = 2.575, Area = 0.9950 ### **Common Critical Values Table:** - **Confidence Level 90%:** Critical Z = 1.645 - **Confidence Level 95%:** Critical Z = 1.960 - **Confidence Level 99%:** Critical Z = 2.576 ### **Additional Notes:** - The tables provide a quick reference to find probabilities and Z-scores without the need for calculation. - “Print” and “Done” buttons are visible, indicating options for output or closure of the screen. This setup aids in the understanding of how Z-scores relate
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