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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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. ---
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,

PX≤a=35%

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