I need the answers for this question please. Thank you Title: Understanding the Distribution of Fat Calorie Percentages in AmericaIntroduction:This exercise explores the distribution of the percentage of fat calories that a person in America consumes each day. It assumes that this percentage is normally distributed with a mean (μ) of 34 and a standard deviation (σ) of 10.Exercise:Let's analyze the distribution and calculate probabilities based on this normal distribution.1. Distribution of X: What is the distribution of \( X \), where \( X \) is the percent of fat calories consumed? \[ X \sim N(\mu, \sigma^2) \] Here, the mean \( \mu = 34 \) and the standard deviation \( \sigma = 10 \). Answer: \( X \sim N(34, 10^2) \)2. Probability Calculation: Find the probability that a randomly selected fat calorie percent is more than 39. Round your answer to 4 decimal places. To find this probability, calculate the Z-score using the formula: \[ Z = \frac{X - \mu}{\sigma} \] Where \( X = 39 \), \( \mu = 34 \), and \( \sigma = 10 \). \[ Z = \frac{39 - 34}{10} = \frac{5}{10} = 0.5 \] Use the Z-table to find the area to the right of Z=0.5. Answer: The probability is approximately 0.3085 (rounded to 4 decimal places).3. Lower Quartile Calculation: Find the minimum number for the lower quartile of fat calories. Round your answer to 2 decimal places. To find the lower quartile (Q1), use the Z-score that corresponds to the 25th percentile. The Z-score for the 25th percentile is approximately -0.675. Convert this Z-score to an X value using the formula: \[ X = \mu + Z \cdot \sigma \] \[ X = 34 + (-0.675) \cdot 10 = 34 - 6.75 = 27.25 \] Answer: The lower quartile is approximately 27.25

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The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 34 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories.

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 34 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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