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Numerade Educator

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Problem 10 Medium Difficulty

The 2007 Current Population Survey reported the following results on U.S. annual household income (in thousands). The survey is a joint effort between the Census Bureau and the Bureau of Labor Statistics.Suppose one household is to be selected at random for a follow-up interview. Find the probability of the following events:
a. The annual household income is $49,999$ or less.
b. The annual household income is $75,000$ or more.
c. The annual household income is between $30,000$ and $99,999$
d. The annual household income is at least $\$ 100,000$

Answer

a. 0.497
b. 0.320
c. 0.495
d. 0.202

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Video Transcript

question for 10. We're given data from the U. S. Census Bureau regarding household income and were asked to provide the probabilities of a randomly selected household having an income that falls within certain ranges. So I've gone ahead and reproduced some of the data in this table. So we have the different brackets of household incomes, and we have the different numbers of households that follow with fall within those brackets. So recall that the probability the empirical probability of event A is equal to the number of instances of event a divided by the total number of Traves so here and is equal to 116,782. So if we were to calculate the probability of an randomly selected household having an annual income of less than $15,000 we could go ahead. Let's let's ease up the notation a little bit, making a little simpler by labelling these events 12 three and so on So we could call that the empirical probability that the income is less than 15,000. All are in other ways to write it like this and is equal to the number in that event So the instances of that event is 15,565 106 divided by the total number, and that probability comes at 20.133 So we can create a probability column. And we can do the same thing for each of these brackets of incomes. And rather than calculate them all for you, I will just go ahead and put the final answers. So then moving on to part A. The question is, what is the probability of a randomly selected household having an income of less than 49,999? So, basically, we're interested in the probability of any of these 1st 3 events taking place, because all of those events are indicative of a household that has a less than $49,999 less than or equal T, so we can write that as probability of one. What's the probability of to it was 0.133 plus the euro 0.170 plus 0.195 comes out to almost almost 50% 0.497 and for B were asked what is the probability that the income is 75,000 or more, so that corresponds to the events. 4326 Part of me that's events five through 6 75,000 or more. Still looking right. That is empirical probability of event five plus the empirical probability of events six. And that equals 0.3 to 0 apart. See, what is the probability of a household having between 30,000 and 99,999? So that is what is the probability of events 34 or five occurring, And that comes out the 0.495 and D S. What is the probability of a randomly selected household having an annual income of greater than or equal to 100,000? So that is, that corresponds to even six alone. So we can just call that empirical probability of event six and then taking that straight from the table. That is the probability of 0.202