Americans receive an average of 18 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 7. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. 77 a. What is the distribution of X? X N 18 b. If an American is randomly chosen, find the probability that this American will receive no more than 21 Christmas cards this year. c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number) Hint: Hint Textbook Pages Submit Question
Americans receive an average of 18 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 7. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. 77 a. What is the distribution of X? X N 18 b. If an American is randomly chosen, find the probability that this American will receive no more than 21 Christmas cards this year. c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number) Hint: Hint Textbook Pages Submit Question
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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I need help with b, c, d
![## Understanding the Distribution of Christmas Cards Received by Americans
In this exercise, we explore the distribution and probabilities associated with the number of Christmas cards received by Americans. Given that Americans receive an average of 18 Christmas cards each year, and this number is normally distributed with a standard deviation of 7, we define \(X\) as the number of Christmas cards received by a randomly selected American.
### Questions and Calculations
**a. What is the distribution of \(X\)?**
\[ X \sim N(18, 7) \]
- \(X\) is normally distributed with a mean (μ) of 18 and a standard deviation (σ) of 7.
**b. If an American is randomly chosen, find the probability that this American will receive no more than 21 Christmas cards this year.**
\[ P(X \leq 21) = \text{(Use the standard normal distribution and z-scores to find this value)} \]
**c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year.**
\[ P(21 \leq X \leq 26) = \text{(Use the standard normal distribution and z-scores to find this value)} \]
**d. 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number)**
\[ \text{Find the 90th percentile of the normal distribution \(N(18, 7)\)} \]
### Hint
For further guidance on solving these problems, refer to the provided textbook pages or click on the hint link for detailed steps.
**Submit Question**
By understanding and correctly applying the properties of normal distribution, you will be able to determine the required probabilities and percentiles. This is a fundamental concept in statistics that has a variety of applications in real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba867a91-7946-4dc8-8b92-57b0d80fa10e%2F435114c8-ce8e-4ec1-a2ee-a76d1927823f%2F1vssrho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Understanding the Distribution of Christmas Cards Received by Americans
In this exercise, we explore the distribution and probabilities associated with the number of Christmas cards received by Americans. Given that Americans receive an average of 18 Christmas cards each year, and this number is normally distributed with a standard deviation of 7, we define \(X\) as the number of Christmas cards received by a randomly selected American.
### Questions and Calculations
**a. What is the distribution of \(X\)?**
\[ X \sim N(18, 7) \]
- \(X\) is normally distributed with a mean (μ) of 18 and a standard deviation (σ) of 7.
**b. If an American is randomly chosen, find the probability that this American will receive no more than 21 Christmas cards this year.**
\[ P(X \leq 21) = \text{(Use the standard normal distribution and z-scores to find this value)} \]
**c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year.**
\[ P(21 \leq X \leq 26) = \text{(Use the standard normal distribution and z-scores to find this value)} \]
**d. 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number)**
\[ \text{Find the 90th percentile of the normal distribution \(N(18, 7)\)} \]
### Hint
For further guidance on solving these problems, refer to the provided textbook pages or click on the hint link for detailed steps.
**Submit Question**
By understanding and correctly applying the properties of normal distribution, you will be able to determine the required probabilities and percentiles. This is a fundamental concept in statistics that has a variety of applications in real-world scenarios.
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