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 2.4 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 ~ N✓ ✓ 55.1 2.4 ▼ Round the following answers to three decimal places. If a Ventura County child is randomly chosen, find the probability that the height is at most 58.7 inches. 0.933 Round the following answer to the nearest integer. The 85th percentile height in Ventura County is how many inches? Enter an integer or decimal number [more..] Part 2 of 3 If a Ventura County child is randomly chosen, find the probability that the height is between 53.9 and 57.5 inches. 0.533 Part 3 of 3

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**Title: Understanding Height Distributions in Ventura County**

In Ventura County, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches and a standard deviation of 2.4 inches. Let \( X \) represent the height of a randomly selected child in Ventura County.

**Distribution:**
- The distribution of \( X \) is denoted by \( X \sim N(55.1, 2.4) \).

**Questions and Probabilities:**

1. **Probability of Maximum Height:**
   - If a Ventura County child is randomly chosen, the probability that their height is at most 58.7 inches is **0.933**.

2. **Probability of Height Within a Range:**
   - If a Ventura County child is randomly chosen, the probability that their height is between 53.9 and 57.5 inches is **0.533**.

**Percentile Information:**

- **85th Percentile Height:**
  - The 85th percentile height in Ventura County is calculated as an integer (requires input).

These calculations illustrate the application of normal distribution in assessing the probabilities related to children's heights in Ventura County.
Transcribed Image Text:**Title: Understanding Height Distributions in Ventura County** In Ventura County, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches and a standard deviation of 2.4 inches. Let \( X \) represent the height of a randomly selected child in Ventura County. **Distribution:** - The distribution of \( X \) is denoted by \( X \sim N(55.1, 2.4) \). **Questions and Probabilities:** 1. **Probability of Maximum Height:** - If a Ventura County child is randomly chosen, the probability that their height is at most 58.7 inches is **0.933**. 2. **Probability of Height Within a Range:** - If a Ventura County child is randomly chosen, the probability that their height is between 53.9 and 57.5 inches is **0.533**. **Percentile Information:** - **85th Percentile Height:** - The 85th percentile height in Ventura County is calculated as an integer (requires input). These calculations illustrate the application of normal distribution in assessing the probabilities related to children's heights in Ventura County.
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