Americans receive an average of 15 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?X N 15 V, 5 b. If an American is randomly chosen, find the probability that this American will receive no more than 18 Christmas cards this year. 0.0666 Enter an integer or decimal number, accurate to at least 4 decimal places (more..] c. If an American is randomly chosen, find the probabili ty that this American will receive between 18 and 21 Christmas cards this year. 0.3849
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Americans receive an average of 15 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? X - N 15
b. If an American is randomly chosen, find the probability that this American will receive no more than 18
Christmas cards this year. 0.0666
Enter an integer or decimal number, accurate to at least 4 decimal places [more..]
c. If an American is randomly chosen, find the probability that this American will receive between 18 and 21
Christmas cards this year. 0.3849
d. 67% of all Americans receive at most how many Christmas cards? (Please enter a whole number)
17
Hint:
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Since we only answer up to 3 sub-parts, we’ll answer the first 3.
Please resubmit the question and specify the other subparts (up to 3) you’d like answered.
a) Given X=the number of Christmas cards received by a randomly selected American.
X follows a normal distribution with mean=15 and standard deviation=5
So, X~N(15,5)
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