people-who-have-some-college-education-fifty-three-percent-of-all-persons-in-the-us-population-have-

Question

People Who Have Some College Education Fifty-three percent of all persons in the U.S. population have
at least some college education. Choose 10 persons at
random. Find the probability that $$
\begin{array}{l}{	ext { a. Exactly one-half have some college education }} \ {b 	ext { . At least } 5 	ext { do not have any college education }} \ {	ext { c. Fewer than } 5 	ext { have some college education }}\end{array}
$$

Danielle Flores · Accepted Answer

53% of people have a college education branch, use 10 people at random, their value of and is 10. And our probability of success is 0.53 for this one success, meaning they have a college education. First question says, What is the probability that exactly half of the people surveyed have a college education? So we&#x27;re looking for the probability that X is equal to five. Since there&#x27;s 10 people surveyed, then half of that would be five. So using the binomial distribution formula, we do 10 factorial, divided by five factorial times five factorial times 0.53 to the fifth power times, 0.47 to the fifth power. We got 0.47 by doing one minus 10.53 That equals 0.47 This would be the probability that they don&#x27;t have some sort of college education. So when we do 10 factorial divided by five factorial times five factorial, you get 252 times 0.53 to the fifth power times 0.47 to the fifth. Power is equal to 0.242 or 24.2%. Remember, you can do this in the cat litter by hitting second bars you will look for by gnome. Pdf is the same equals 25 You do 10 0.53 and five and you would get 0.242 What if the question says at least five do not get a college education? So we&#x27;re looking for What is the probability that X is greater than or equal to five? And this one we&#x27;re looking for do not have some sort of college education. So therefore, you wanna look at the the other probability of 0.47 because 0.53 says they have some sort of college education. 0.47 says they have no college education. We&#x27;re gonna dio one minus by gnome CDF our sample sizes 10. Our probability for this one is 0.47 and we are looking for greater than or equal to five. So we do less than or equal to four. This probability will tell us less than or equal to four, and we subtract that from one to get all the numbers that are greater than then four. When I do that, you still use the same function in the Cacador second bars, you&#x27;ll see by gnome CDF and you get 0.547 or 54.7%. You could do this by hand, but you&#x27;re gonna have to find the probability that X equals 56789 10 And add them all together and you get the same answer. What is the probability Probability that fewer than five have a college education. To do that, you&#x27;re looking for the probability that X is less than five. So I can do the probability of X equals zero plus the probability of X equals one, plus the probability of X equals two all the way up to the probability the X equals four. I don&#x27;t include five in this one because it just says fewer than five have a college education. If I could do all of that by hand, using the binomial formula or I can use the Bynum, he will live distribution function. And I would you 10 0.53 and four, cause I&#x27;m looking for the sum of all the probabilities from 0 to 4. I do that in the keg bitter. I get 0.306 which is 30.6%

Lourence Gonhovi · Answer

So the probability expressed in simplified faction that the randomly selected American edged 25 for above not completed four years off college is now. You can take a reference to the diagram keeping question. Uh, now you can see that to wic whole. The numbers that you guys off high school. They&#x27;re less than four years off my school and already complained a lot off working. So the best way to do it is just to find those we have completed before year, Uh, college, and then some clicked show. Mom, I want to get the compliment, and that will be our ask. So So the probability Oh, uh, greater than four years is equal to one minus. Now we look att, the probability off Those were finished college program, which is four years or great in the 40 five in total, divided by the torta for the experiment or the sample space, which is under the 74. So if you subtract one minus 45 4 from 74 you will get 129 divided by 1 74 and you can divide by three three into 12. It caused four times three into line because three times playing into 17 It caused five times is, uh, remained off too. Three into train before that age, so simplified the hands off the 43 divided by 58.

Lourence Gonhovi · Answer

find. The probability it&#x27;s pressed is a simplified fraction that randomly selected American age 25 over yes completed four years of high school only on less than four years of college. So what we need to do is to combine, because once they put or they want us to combine those, the fest event is, um so we can call it in. We choose in, he&#x27;s exists. This is high school, and then the total is, um, 56. And then we also have got an F. It&#x27;s call it F, which is, ah, completed less than four years off college, and the total is 44. So what we want is a combined oh about ability, which is 56 last 44 divided by 174 which is Han drugs divided by once before, which is true in 215 Tilly into accident D for its ah 87

Lourence Gonhovi · Answer

All right. Um, the probability that a randomly selected American Age 25 over has not completed four years of high school is now You have to also take their friends today. Uh, temple provided and, uh, in the column. For less than four years, I school you realize that the Tatar is twin. Did mine. So physically, a probe ability off less than four years. High school is equal to the total, for those is 29. That is 14 last 15 uh, divided by the total fumble space, which is handled end 74 now 29 easy faked off ones and 94. So between the men between did nine. It&#x27;s one divided by 29 1 74 goes six stripes. So the probability off those that, if not completed four years off high school is one or six

Lourence Gonhovi · Answer

find the probability that a randomly selected American age two undefined ful over it&#x27;s computed less than four years off I school. All four is less than four years off my school or four years off my school, so we wanted to combine those two columns. The Four Years column. Patel is 29 so we can college E so I can just say let that they let that torture of the in the desperate in total off 29 can have on literally quality F would have called it a or B, huh? 56 is the total for the two columns that all and ah probability that we are combining those two eases. Ah will give us addition off the tube, which is 85 divided by the Total Assemble space, which is under 74.

Evelyn Cunningham · Answer

Let&#x27;s start with what we know in this particular problem, we have 10 people applying for a job, So we have 10 applicants. Of those 10 5 have college degrees and five don&#x27;t. And we are going to look at three applicants set random, and we&#x27;re going to focus on getting college graduates. So let&#x27;s look at what our probability distribution would look like. So when we look at these applicants and we select, we might end up with zero college grads, we might end up with one or two or three. Now, that&#x27;s the entire probability distribution. So the sum of our p of X column should equal one. Now, what are we trying to find when we actually higher? If the manager selects thes three applicants, we want the probability that all three were graduates. So we&#x27;re solely focused on this value right here. So our X value is three. Now, once we select a person to be the person that gets the job, we&#x27;re not gonna put them back into the pool of people. So therefore our sampling is done without replacement. So because of the sampling is done without replacement, we&#x27;re talking a about a hyper geometric distribution. And there&#x27;s a formula that governs hyper geometric distributions. And that formula reads the combination of a items taken exit a time multiplied by the combination of be items taken n minus X at a time all over a plus B items taken and at a time and a represents the count of favourable options. So in this case, we&#x27;re looking for college grads. So are a value is going to be five and b represents the unfavourable count. And in this case, we don&#x27;t want the ones with college degrees. So they&#x27;re the unfavourable. So be is going to take on a value of five. So we have all the information we have need to use this formula. We have an end value. We haven&#x27;t X value, even a value and a B value. So we&#x27;re ready to substitute in. So therefore, it would read the combination of five taken three at a time, multiplied by the combination of five taken the re minus three at a time all over five plus five combination taken three at a time. So now we can clean that up a little bit before we pick up our calculator. So it be five C three multiplied by five C zero all over 10. See three. And if you put that into your calculator, you will end up with a fraction that reads 10 for the numerator and 100 20 in the denominator, which reduces into 1 12 So the probability of getting three college grads when we select the applications at random would be one 12th. And if you want to do, you can put it into its decimal equivalent, which is approximately 0.83 and your answer would be 0.83 or window.

Problem

Guidance Missile System A missile guidance system…

Problem 15 Hard Difficulty

Answer

a. 0.242
b. 0.547
c. 0.306

Related Courses

Elementary Statistics a Step by Step Approach

Related Topics

Discussion

Top Intro Stats / AP Statistics Educators

Catherine R.

Boris M.

Michael J.

Joseph L.

Intro Stats / AP Statistics Courses

Data And Variables

Data And Variables - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 5

Video Transcript

Allan G. Bluman

Elementary Statistics a Step by Step Approach

Catherine R.

Boris M.

Michael J.

Joseph L.

Data And Variables

Data And Variables - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

a. 0.242b. 0.547c. 0.306

Elementary Statistics a Step by Step Approach

Catherine R.

Boris M.

Michael J.

Joseph L.

Data And Variables

Data And Variables - Example 1

Allan G. BlumanElementary Statistics a Step by Step Approach

Catherine R.

Boris M.

Michael J.

Joseph L.

a. 0.242
b. 0.547
c. 0.306

Allan G. Bluman

Elementary Statistics a Step by Step Approach