Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with u: and o = 27. (a) What proportion of children aged 13 to 15 years old have scores on this test above 93 ? (NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.) Answer: (b) Enter the score which marks the lowest 20 percent of the distribution. Answer: (C) Enter the score which marks the highest 10 percent of the distribution. Answer:
Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with u: and o = 27. (a) What proportion of children aged 13 to 15 years old have scores on this test above 93 ? (NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.) Answer: (b) Enter the score which marks the lowest 20 percent of the distribution. Answer: (C) Enter the score which marks the highest 10 percent of the distribution. Answer:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![**Educational Content on Normal Distribution and Percentiles**
Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with a mean (\(\mu\)) of 111 and a standard deviation (\(\sigma\)) of 27.
**Questions:**
(a) **What proportion of children aged 13 to 15 years old have scores on this test above 93?**
*(NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.)*
**Answer:**
[Input Box]
(b) **Enter the score which marks the lowest 20 percent of the distribution.**
**Answer:**
[Input Box]
(c) **Enter the score which marks the highest 10 percent of the distribution.**
**Answer:**
[Input Box]
---
**Explanation:**
- **Normal Distribution:** A continuous probability distribution characterized by a symmetric, bell-shaped curve, defined by the mean (\(\mu\)) and standard deviation (\(\sigma\)).
- **Percentile:** Represents the value below which a given percentage of observations in a group falls. For example, the 20th percentile is the value below which 20% of the observations may be found.
To solve these questions, one might use a standard normal distribution table (Z-table) or statistical software to find the corresponding Z-scores and percentiles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa00d0151-b5df-4ee3-a0d6-fdfba7d1c4f7%2Fef5d37d6-024d-43cb-b16c-70fb46163409%2Fe8hgo3l_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content on Normal Distribution and Percentiles**
Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with a mean (\(\mu\)) of 111 and a standard deviation (\(\sigma\)) of 27.
**Questions:**
(a) **What proportion of children aged 13 to 15 years old have scores on this test above 93?**
*(NOTE: Please enter your answer in decimal form. For example, 45.23% should be entered as 0.4523.)*
**Answer:**
[Input Box]
(b) **Enter the score which marks the lowest 20 percent of the distribution.**
**Answer:**
[Input Box]
(c) **Enter the score which marks the highest 10 percent of the distribution.**
**Answer:**
[Input Box]
---
**Explanation:**
- **Normal Distribution:** A continuous probability distribution characterized by a symmetric, bell-shaped curve, defined by the mean (\(\mu\)) and standard deviation (\(\sigma\)).
- **Percentile:** Represents the value below which a given percentage of observations in a group falls. For example, the 20th percentile is the value below which 20% of the observations may be found.
To solve these questions, one might use a standard normal distribution table (Z-table) or statistical software to find the corresponding Z-scores and percentiles.
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