5

(1+3+3_12 points) In My class there are 140 students From mny past experience know that the probability of student showing up is 0.82_ One day prepared handout and ...

Question

(1+3+3_12 points) In My class there are 140 students From mny past experience know that the probability of student showing up is 0.82_ One day prepared handout and made 120 copies Let Y be the nutnber of students ho showed up that day: You ACSunC that students act independently: a) How is distributed? b) Find the probability that had cnough handouts for the entire class Find the probability that had lcast students did not Bel copy of the handout.

(1+3+3_12 points) In My class there are 140 students From mny past experience know that the probability of student showing up is 0.82_ One day prepared handout and made 120 copies Let Y be the nutnber of students ho showed up that day: You ACSunC that students act independently: a) How is distributed? b) Find the probability that had cnough handouts for the entire class Find the probability that had lcast students did not Bel copy of the handout.



Answers

One student is selected at random from a group of 200 students known to consist of 140 full-time $(80 \text { female and } 60 \text { male })$ students and 60 part-time (40 female and 20 male) students. Event $A$ is "the student selected is full time," and event $\mathrm{C}$ is "the student selected is female." a. Are events $A$ and $C$ independent? Justify your answer. b. Find the probability $P(\mathrm{A} \text { and } \mathrm{C}$ ).

This question asked us to answer the various probabilities we know for part. A six of the 30 students are left handed and five of the remaining 29 students are left handed. Therefore, what we know is that if we multiply these fractures together, we end up with 1/29 for part B. What we know by looking at this is that 24 of the 30 students are right handed. 23 of the remaining 29 are right handed Multiplying these Together we get 92/1 45 for part C. We know that 24 of the 30 students are right handed. Six of the remaining 29 students are left tended multiplying these together we end up with 24/1 45.

This problem or given a table, and we need to use the information on the table to answer the six questions. So part A. What is the probability that this person will be female when we have 700 females altogether? So that will be 700 over a total of 1500 students, so ah, that will reduce to 7/15 in Part B. We want a grade 12 male. So we ah, look at the table. There are 220 grave 12 males, so that will be 2 20 over 1500 total students. And when we reduce this, that will be 11/75 in part c Ah, they've got it worded in a different way. But essentially, that's asking you the probability of being a great 12 student, given that we know their female already. So using the conditional probability formula would be probability of grade 12 and female over probability of female. So Ah, great. 12 and female. We have 180 out of 1500 and probability of female is 700 Notre 1500. So when we reduce this, we will get 9/35 uh, in the next question we want Grade 12 or female. So, uh, we see that there are 400 grade twelves altogether and, um, 700 females old together, but we've double counted the 1 80 So, uh, essentially, it'll be, um, to 20 less 1 80 plus 1 90 less 1 30 plus 200 divided by 1500. So when we out all of that up, that will work out to 9 20 and divided by 1500 reduce That will be 46/75 and heart e again, they haven't worded differently, But essentially, it's asking you to find the probability that it's a male student, given that there in grade 12 so conditional probability, probability of male and Grade 12 over probability of great 12 and male and grade 12. That's 220 out of 1500 over probability of grade 12. We have 400 out of 1500 and when we simplify, that will work out to 11/20. And f um are the genders and grades independent so we can just zone and on, um great 12 males again, since we've been working with that quite a few times here um so if independent ah probability. Ah, male times probability of grade 12 should equal to, ah, probability of male and grade 12 male in grade 12. We did in part B. That was 11/75 but I'll one reduce it. That was 2 20 over 1500. That's been part B. Let's take a look and see if this works up a male that would be 800 out of 1500 and ah, great 12. We had 400 out of 1500. So when we multiply, this works out to 32/2. 25. This one on the right side works at 11/75 so we see that they are not equal to each other. Hence they are not independent.

So here we have a number of students 200 total, and we know that 108 took English. 138 took statistics and then 70 took both. Now, if we're toe ad, those three numbers up, we would get a number greater than 200. And that's because since we know 70 took both English and statistics, the individual subject count double counts the students who took both English and statistics. So if we're to create a Venn diagram or students taking English and statistics, we know that 70 would be in the middle because thes students took both English and statistics now to fill out the rest of even diagram you to figure out how many students took just statistics and just English what we know for English, the total has to be 108 and we have 7 70 of them already counted. So we will subtract 70 from 108 and we will get 38. So 38 students just took English. Do the same process for statistics will take 138 and subtract 70 from that and we will get 68 so 68 students just took statistics. And when you add those three numbers up, we get a number that is less Stan 200. We get 1 76 And so when we subtract 1 76 from 200 we get 24 students. So we know that 24 students did not take either, so they took neither. Now we have all the information we need to figure out our probabilities. So our first probability is the probability that they takes English or statistics. So we don't want the students we took both. We want either English or statistics, so we know where denominator is gonna be out of 200. Because that's the total number of students. And we just figured out the students that just took English was 38 the English that just took statistics with 68. So we will add those two numbers together and we get 106. So there's 100 6 students that just just took one of the two subjects, and that is the probability that a student takes English or statistics. Our next probability is what is it? Probably a student took neither last. Well, we already figured out that 24 students were left over from the spend diagram. So 24 of the 200 students did not take either statistics or English. And lastly, we want the probability of student takes statistics, but not English. Well, that's just gonna be the number 68 because they just have statistics. They didn't take both, and we know that they did not take English, so our final probability will be 68 out of 200.

So we're given a population of 200 students in the class, and we know that 108 took English. 138 took statistics, and 70 took both classes so we can solve this using a been diagram. And so we know that 70 students took both English and statistics so we can write 70 in our little overlap here now, when we have that English has 108 students and statistics has 138 students. That count includes the 70 students that are taking both. So, in order to figure out students that just took English or a justice statistics, we have to subtract 70 both of those counts. So we'll take 108 and subtract 70 and we will get 38 English students that just took English, and we'll do the same thing for a statistics would take 138 and subtract 70 and we will get 68 students that just took statistics. And if we add all those numbers individually, 70 plus 38 68 will have 176 students took either of those classes so far. First probability we want. Probably do. They took English or statistics? Well, we know that 176 students either took just English justice ticks or both. So the probability here is 176 out of the total number of students, which is 200. Then we want the probability that a student took neither English or statistics. Well, just like I mentioned, we have 176 students who took either one class or both. So we subtract 176 from 200. We will get 24 students did not take either English statistics or both. So the probability that we select a students who took either class is 24 out of our total of 200. Then we want the probability that the student took Excuse me, took statistics but not English. So that's where this Red 68 comes in. 68 Soon's just took statistics without taking English, so that probability is now 68 out of a total of 200


Similar Solved Questions

5 answers
Calculate the de Broglie wavelength in meters of a tennis ball with mass of 9.00 10 2kg that has kinetic energy of 6.53 107 J. (Answer; |.93 10-37 m )
Calculate the de Broglie wavelength in meters of a tennis ball with mass of 9.00 10 2kg that has kinetic energy of 6.53 107 J. (Answer; |.93 10-37 m )...
5 answers
Complete the table by computing f(x) at the given values of x {Round your answers to three decimal places.10010001001000Use the results t0 guess at the indicated limits, they exis: (If an answer does not exist, enter DNE:)lim f ()limI + 8
Complete the table by computing f(x) at the given values of x {Round your answers to three decimal places. 100 1000 100 1000 Use the results t0 guess at the indicated limits, they exis: (If an answer does not exist, enter DNE:) lim f () lim I + 8...
5 answers
For the pair of functions, find the indicated composition: f(x) = +6 +9, g(x)=vx-9Find (g f)(x).
For the pair of functions, find the indicated composition: f(x) = +6 +9, g(x)=vx-9 Find (g f)(x)....
5 answers
Use the equation f(x) dx = 1(+21(4) to evaluate the following definite integral: 070j> dx,a< bRewrite the limit using the integrand 1, dx =Iim 2 neon K41Expand and evaluate the limit What is the result?dx=
Use the equation f(x) dx = 1(+21(4) to evaluate the following definite integral: 070 j> dx,a< b Rewrite the limit using the integrand 1, dx =Iim 2 neon K41 Expand and evaluate the limit What is the result? dx=...
5 answers
Match the experiment with its probable outcome_ Use each term only onceanimal cal cells placed on top of vegetal tissueChoose:.. epidermis cells from the dorsal margin of a blastula ventral mesoderm undifferentiated endoderm vegetal cells allowed to develop alone in culture dorsal mesoderm mesoderm cells from the ventral margin of a blastulaan animal cap allowed to develop alone in culture Choose ..
Match the experiment with its probable outcome_ Use each term only once animal cal cells placed on top of vegetal tissue Choose:.. epidermis cells from the dorsal margin of a blastula ventral mesoderm undifferentiated endoderm vegetal cells allowed to develop alone in culture dorsal mesoderm mesoder...
5 answers
Other? of information avehac maintained U segre gated andparacellular cells in the fhose cells Visuroceste 1 1 and how are those these 1 1
other? of information avehac maintained U segre gated andparacellular cells in the fhose cells Visuroceste 1 1 and how are those these 1 1...
5 answers
Evaluate the integral:Vy? - 81 L dy, y> 9Which substitution transforms the given integral into one that can be evaluated directly in terms of 0?0 A y=9 sin 0 0 B. y =9 tan 0sec 0Given the expression for above find dy in terms of 0 andEvaluate the integraldy =
Evaluate the integral: Vy? - 81 L dy, y> 9 Which substitution transforms the given integral into one that can be evaluated directly in terms of 0? 0 A y=9 sin 0 0 B. y =9 tan 0 sec 0 Given the expression for above find dy in terms of 0 and Evaluate the integral dy =...
5 answers
Find the value of the definite integral, if exists. (Not a calculator problem!) Exact answer, no decimal approximation. [cos(x ')].x dx
Find the value of the definite integral, if exists. (Not a calculator problem!) Exact answer, no decimal approximation. [cos(x ')].x dx...
1 answers
Solve each problem. Mr. Armas is a sales associate for a computer company. He receives a salary plus a bonus for any computer package he sells. Find Mr. Armas' bonus if he sells 16 computer packages. $$\begin{array}{|c|c|}\hline \text { Packages } & \text { Bonus } \\\hline 2 & \$ 100 \\\hline 4 & \$ 125 \\\hline 6 & \$ 150 \\\hline 8 & \$ 175 \\\hline\end{array}$$
Solve each problem. Mr. Armas is a sales associate for a computer company. He receives a salary plus a bonus for any computer package he sells. Find Mr. Armas' bonus if he sells 16 computer packages. $$\begin{array}{|c|c|}\hline \text { Packages } & \text { Bonus } \\\hline 2 & \$ 100 \...
5 answers
Consider the level surface f(x, Y, 2) 48 for f(x, Y, 2) = Ax2 2y2 + 22 at point (4, 4, 4).(a) Find the equation of the tangent plane_(b) Find the normal line to the given surface at the given point:X_ 8 -Y34 = 232Y34 -242Y4 2 _ 4Y4 2 +
Consider the level surface f(x, Y, 2) 48 for f(x, Y, 2) = Ax2 2y2 + 22 at point (4, 4, 4). (a) Find the equation of the tangent plane_ (b) Find the normal line to the given surface at the given point: X_ 8 -Y34 = 232 Y34 -242 Y4 2 _ 4 Y4 2 +...
4 answers
1) About ______% of the area under the curve of thestandard normal distribution isbetween z=−1.609z=-1.609 and z=1.609z=1.609 (orwithin 1.609 standard deviations of the mean).2) About _______% of the area under the curve of thestandard normal distribution is outside theinterval z=[−2.38,2.38]z=[-2.38,2.38] (or beyond 2.38standard deviations of the mean).
1) About ______% of the area under the curve of the standard normal distribution is between z=−1.609z=-1.609 and z=1.609z=1.609 (or within 1.609 standard deviations of the mean). 2) About _______% of the area under the curve of the standard normal distribution is outside the interval z=[âˆ...
5 answers
Question below
Question below...
5 answers
6 Show f(x)ez and g(c)rer linearly independent by finding its Wronskian.
6 Show f(x) ez and g(c) rer linearly independent by finding its Wronskian....
5 answers
The null hypothesis:Ko 0The altemative hypothesis:The type of test statistic:(Choose oneThe value of the test statistic: (Round to at least three decimal placesThe p-value (Round to at least three decimal places_Can we 'aumpeorcfthe easing ficm" 9 clain thatthe mean cf miles driven annually Is less than 13620 miles?TesNo
The null hypothesis: Ko 0 The altemative hypothesis: The type of test statistic: (Choose one The value of the test statistic: (Round to at least three decimal places The p-value (Round to at least three decimal places_ Can we 'aumpeorcfthe easing ficm" 9 clain thatthe mean cf miles driven ...
5 answers
What is change in entropy at STP for the following reaction? FezOs +3C0 (g) ~ 3C02(g) + 2Fe (s)Substance Fe_Os(s) co(g) COx(g)AG" (kJmol) -741.0 -137.2 -394.4AHP (kJmol) 822.2 -10.5 ~3935
What is change in entropy at STP for the following reaction? FezOs +3C0 (g) ~ 3C02(g) + 2Fe (s) Substance Fe_Os(s) co(g) COx(g) AG" (kJmol) -741.0 -137.2 -394.4 AHP (kJmol) 822.2 -10.5 ~3935...

-- 0.017204--