Americans receive an average of 17 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 5. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? XN(17 b. If an American is randomly chosen, find the probability that this American will receive no more than 21 Christmas cards this year. 5 c. If an American is randomly chosen, find the probability that this American will receive between 19 and 23 Christmas cards this year. d. 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Title: Understanding the Distribution of Christmas Cards Received

Description: Americans receive an average of 17 Christmas cards each year, with the number of cards being normally distributed and a standard deviation of 5. Let \(X\) represent the number of Christmas cards received by a randomly selected American. For accurate calculations, answers are rounded to four decimal places.

Questions:

a. Distribution of \(X\):
   - What is the distribution of \(X\)? 
   - \(X \sim N(17, 5)\)

b. Probability of Receiving No More Than 21 Cards:
   - If an American is randomly chosen, find the probability that this individual will receive no more than 21 Christmas cards this year.
   - [To be calculated]

c. Probability of Receiving Between 19 and 23 Cards:
   - If an American is randomly chosen, find the probability that this individual will receive between 19 and 23 Christmas cards this year.
   - [To be calculated]

d. Maximum Number of Cards Received by 90% of Americans:
   - 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number)
   - [To be calculated]
Transcribed Image Text:Title: Understanding the Distribution of Christmas Cards Received Description: Americans receive an average of 17 Christmas cards each year, with the number of cards being normally distributed and a standard deviation of 5. Let \(X\) represent the number of Christmas cards received by a randomly selected American. For accurate calculations, answers are rounded to four decimal places. Questions: a. Distribution of \(X\): - What is the distribution of \(X\)? - \(X \sim N(17, 5)\) b. Probability of Receiving No More Than 21 Cards: - If an American is randomly chosen, find the probability that this individual will receive no more than 21 Christmas cards this year. - [To be calculated] c. Probability of Receiving Between 19 and 23 Cards: - If an American is randomly chosen, find the probability that this individual will receive between 19 and 23 Christmas cards this year. - [To be calculated] d. Maximum Number of Cards Received by 90% of Americans: - 90% of all Americans receive at most how many Christmas cards? (Please enter a whole number) - [To be calculated]
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