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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Question

The probability is? 

### Understanding Probability in Normal Distribution **Problem Statement:** Assume that a randomly selected subject is given a bone density test. These test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than -1.01 and draw a sketch of the region. **Task:** - **Sketch the region.** Choose the correct graph that represents this probability. **Options:** - **Graph A:** A normal distribution curve shaded to the left of 1.01. - **Graph B:** A normal distribution curve shaded to the right of -1.01. - **Graph C:** A normal distribution curve shaded between -1.01 and 1.01. - **Graph D:** A normal distribution curve shaded to the left of -1.01. (Selected as the correct graph) **Explanation of Graph D:** Graph D displays a bell-shaped curve representing a standard normal distribution. The area to the left of the vertical line at -1.01 is shaded, indicating the probability of a score being less than -1.01. This shaded region signifies the cumulative probability from negative infinity up to -1.01. **Conclusion:** To find the probability, use statistical tables or software for the standard normal distribution to identify the corresponding probability for the z-score of -1.01. - **Note:** The probability is calculated and rounded to four decimal places.
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Transcribed Image Text:### Understanding Probability in Normal Distribution **Problem Statement:** Assume that a randomly selected subject is given a bone density test. These test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than -1.01 and draw a sketch of the region. **Task:** - **Sketch the region.** Choose the correct graph that represents this probability. **Options:** - **Graph A:** A normal distribution curve shaded to the left of 1.01. - **Graph B:** A normal distribution curve shaded to the right of -1.01. - **Graph C:** A normal distribution curve shaded between -1.01 and 1.01. - **Graph D:** A normal distribution curve shaded to the left of -1.01. (Selected as the correct graph) **Explanation of Graph D:** Graph D displays a bell-shaped curve representing a standard normal distribution. The area to the left of the vertical line at -1.01 is shaded, indicating the probability of a score being less than -1.01. This shaded region signifies the cumulative probability from negative infinity up to -1.01. **Conclusion:** To find the probability, use statistical tables or software for the standard normal distribution to identify the corresponding probability for the z-score of -1.01. - **Note:** The probability is calculated and rounded to four decimal places.
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