In Ventura County, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 3.7 inches. Let X be the height of a randomly chosen child in Ventura County. Binomial: B, Uniform: U, Normal: N What is the distribution of X? X~ NV 55.1 ✓, 3.7 ▼ Part 2 o Round the following answers to three decimal places. If a Ventura County child is randomly chosen, find the probability that the height is more than 45.8 inches 0.994
In Ventura County, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 3.7 inches. Let X be the height of a randomly chosen child in Ventura County. Binomial: B, Uniform: U, Normal: N What is the distribution of X? X~ NV 55.1 ✓, 3.7 ▼ Part 2 o Round the following answers to three decimal places. If a Ventura County child is randomly chosen, find the probability that the height is more than 45.8 inches 0.994
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Normal Distribution of Heights in Ventura County**
In Ventura County, the height measurements of ten-year-old children are approximately normally distributed. The distribution has a mean of 55.1 inches and a standard deviation of 3.7 inches. Let \( X \) be the height of a randomly chosen child in Ventura County.
**Distribution of \( X \)**
The height \( X \) is normally distributed:
\[ X \sim N(55.1, 3.7) \]
---
**Probability Calculations**
*Round the following answers to three decimal places.*
1. **Probability that height is more than 45.8 inches:**
If a Ventura County child is randomly chosen, the probability that the height is more than 45.8 inches is:
\[ \text{Probability} = 0.994 \]
2. **Probability that height is between 53.2 and 55.1 inches:**
If a Ventura County child is randomly chosen, the probability that the height is between 53.2 and 55.1 inches is:
\[ \text{Probability} = 0.196 \]
---
**Percentile Calculation**
*Round the following answer to the nearest integer.*
- **35th Percentile Height:**
To find the 35th percentile height in Ventura County, calculate the value (not percentage). Use statistical software (like R) and apply the z-score. Enter the percentile value once calculated.
**Hint:** You are looking for the exact height that corresponds to the 35th percentile, starting with R and utilizing the z-score for computation.
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Transcribed Image Text:**Normal Distribution of Heights in Ventura County**
In Ventura County, the height measurements of ten-year-old children are approximately normally distributed. The distribution has a mean of 55.1 inches and a standard deviation of 3.7 inches. Let \( X \) be the height of a randomly chosen child in Ventura County.
**Distribution of \( X \)**
The height \( X \) is normally distributed:
\[ X \sim N(55.1, 3.7) \]
---
**Probability Calculations**
*Round the following answers to three decimal places.*
1. **Probability that height is more than 45.8 inches:**
If a Ventura County child is randomly chosen, the probability that the height is more than 45.8 inches is:
\[ \text{Probability} = 0.994 \]
2. **Probability that height is between 53.2 and 55.1 inches:**
If a Ventura County child is randomly chosen, the probability that the height is between 53.2 and 55.1 inches is:
\[ \text{Probability} = 0.196 \]
---
**Percentile Calculation**
*Round the following answer to the nearest integer.*
- **35th Percentile Height:**
To find the 35th percentile height in Ventura County, calculate the value (not percentage). Use statistical software (like R) and apply the z-score. Enter the percentile value once calculated.
**Hint:** You are looking for the exact height that corresponds to the 35th percentile, starting with R and utilizing the z-score for computation.
---
Expert Solution
Step 1
Let us denote the value at 35th percentile as a.
That is, the 35th percentile is,
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Solved in 2 steps
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