This is a normal distribution problem **Title: Understanding Caloric Consumption Distribution at a Buffet****Introduction:**The caloric intake of customers at a Chinese buffet is analyzed under the assumption of a normal distribution. The average (mean) calorie consumption is 2927 calories, with a standard deviation of 654 calories. This information helps to understand the eating patterns and the variability among different customers.**Questions:****a. Determine the Distribution of X:** The random variable X represents the number of calories consumed by a customer. Given the parameters, the distribution of X can be expressed as $ X \sim N(\mu, \sigma^2) $ where:- $ \mu $ is the mean = 2927- $ \sigma $ is the standard deviation = 654**b. Probability of Consuming Less than 2768 Calories:** Calculate the probability that a randomly selected customer consumes fewer than 2768 calories. This involves finding the area under the normal distribution curve to the left of 2768 calories.**c. Proportion of Customers Consuming Over 3179 Calories:** Determine what proportion of customers exceed a caloric consumption of 3179 calories. This is equivalent to calculating the area under the normal distribution curve to the right of 3179 calories.**Conclusion:**This exercise in statistical analysis provides insight into customer behavior and helps in understanding patterns in caloric consumption, which could be valuable for buffet management and health-related studies. All calculations should be rounded to four decimal places where necessary for precision.

Answered: Image /qna-images/answer/e080cb91-8ad7-4f06-9b62-5556eb6a92f1.jpg

Answered: The amount of calories consumed by…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

This is a normal distribution problem

**Title: Understanding Caloric Consumption Distribution at a Buffet**

**Introduction:**

The caloric intake of customers at a Chinese buffet is analyzed under the assumption of a normal distribution. The average (mean) calorie consumption is 2927 calories, with a standard deviation of 654 calories. This information helps to understand the eating patterns and the variability among different customers.

**Questions:**

**a. Determine the Distribution of X:**
The random variable X represents the number of calories consumed by a customer. Given the parameters, the distribution of X can be expressed as $ X \sim N(\mu, \sigma^2) $ where:
- $ \mu $ is the mean = 2927
- $ \sigma $ is the standard deviation = 654

**b. Probability of Consuming Less than 2768 Calories:**
Calculate the probability that a randomly selected customer consumes fewer than 2768 calories. This involves finding the area under the normal distribution curve to the left of 2768 calories.

**c. Proportion of Customers Consuming Over 3179 Calories:**
Determine what proportion of customers exceed a caloric consumption of 3179 calories. This is equivalent to calculating the area under the normal distribution curve to the right of 3179 calories.

**Conclusion:**

This exercise in statistical analysis provides insight into customer behavior and helps in understanding patterns in caloric consumption, which could be valuable for buffet management and health-related studies. All calculations should be rounded to four decimal places where necessary for precision.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step by step

Solved in 3 steps with 22 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions