a high school randomly selected 75 of the 200 seniors

Using the formulas, calculate the (i) mean and (ii) standard deviation of $X$. I'll say 0.10 and so the probability that in Direct link to Kaitlyn Anderson's post How we would solve this i, Posted 4 years ago. going to be equal to the square root of P times one minus Three characteristics of a binomial experiment, The outcomes of a binomial experiment fit a binomial probability distribution. is 15%, which they tell us up here, they say 15% of How would I do this if I were to standardize the distribution? Given the frequency table below for a list of recorded lengths (in inches) of randomly sampled garden snakes, find the mean. 4 13 12 . (P#z_ fd: SSV6jSc_sIqMApe' .DOCf3ryX@)\ how do we decide this? Answer on Question #61215 - Math - Statistics and Probability Question A) The weight of the adult females has a mean around 60 kg and a standard deviation of 20kg. Let $X =$ the number of heads in 15 flips of the fair coin. endstream endobj 47 0 obj <>stream Compute the population mean $\mu$. Free 1-week access to over 20 lesson videos and 20 practice questions. All are free! So the way that we're going the approximate probability that more than 10% of the Ht[O0)g"Ix+Mah .d-S.~NJ\~*pRC!U19>jO0:9:pQS'a%',$d2LL. endstream endobj 41 0 obj <>stream Standard Deviation $= \sqrt{npq} = \sqrt{80(0.613)(0.387)} \approx 4.3564$, $P(x > 50) = 1 P(x \leq 50) = 1 \text{binomcdf}(80, 0.613, 50) = 1 0.6282 = 0.3718$, Access to electricity (% of population), The World Bank, 2013. He surveys 125 randomly selected homeowners to determine whether or not they own dogs. can answer this on your own. Estimate the sample mean. Since the coin is fair, $p = 0.5$ and $q = 0.5$. There are only two possible outcomes, called "success" and, "failure," for each trial. Let $X$ = the number of people who will develop pancreatic cancer. This is not binomial because the names are not replaced, which means the probability changes for each time a name is drawn. Frequency ..Midpoint Sum of Midpoint. than 0.10 just like that. There are lots of these on the web. Think of trials as repetitions of an experiment. Direct link to Bryan's post If you think about it, th, Posted 5 years ago. Can someone please help with the question above? Estimate the true portion of high school graduates in this region who; The student body of a large university consists of 40% female students. The names of all committee members are put into a box, and two names are drawn without replacement. If you were taking this on Which of the following represents the population in the scenario below? answer choices . Subsequently, they find that 0000011466 00000 n What is the probability that the chairperson and recorder are both students? Let $X =$ the number of pages that feature signature artists. Why does Mister Mxyzptlk need to have a weakness in the comics? A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Example 6.9. The probability that at most 12 workers have a high school diploma but do not pursue any further education is 0.9738. 0000011226 00000 n Probability that students passed in statistics = 25/125 Each game you play is independent. 15. randomly selected high school seniors, the mean score on a standardized test was. 1. $X \sim B(20, 0.41)$, Find $P(x \leq 12)$. If the sample of 16 adult females was chosen. The International Shark Attack File recorded the number of shark attacks between 1837 and 2016 for 9 different U.S. states. So this is approximately 0.96 0000009938 00000 n endstream endobj 42 0 obj <>stream example, your town or city governments Public Works Department might Then find the probability that a student selected at random from the class has passed in only one subject . Available online at, NBA Statistics 2013, ESPN NBA, 2013. I am not able to understand how the set 3 - 5 - 6 - 7 - 13 - 17 - 35 has been derived. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The best answers are voted up and rise to the top, Not the answer you're looking for? Please note, your answers may differ a bit based on how . rev2023.3.3.43278. 0000003688 00000 n and if it is, then we can use its mean and the standard right over here of, so this is the mean, of our sampling I know that sampling distribution is taking a lot of sample and calculate their statistics, while binomial distribution may only have one sample and the distribution we use is related to population. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. hbbd```b``z"A$ I0&v0&e0\ 6'D6' H2V , e("30 A "success" could be defined as an individual who withdrew. A retail company has 50 large stores located in different areas throughout a state. According to U.S. climate data, the monthly average high temperatures, in degrees Fahrenheit, for the city of Chicago are listed below. Let n(M) = 70 ( students passed in mathematics) ; n(S) = 55 ( students passed in Statistics) ; n(M $\cap S) = 30.$, Therefore, probability of students passed in mathematics = $\frac{70}{125}; $, Probability of students passed in statistics = = $\frac{55}{125}; $, Using $$P(M \cup S) = P(M) + P(S) - P(M \cap S)$$, $$\Rightarrow P(M \cup S) = \frac{70}{125} + \frac{55}{125} - \frac{30}{125} = \frac{19}{25}$$, But the answer is wrong ; book answer is : $\frac{13}{25}$. So pause this video and see suppose that 15% of the 1,750 students at a school have 0000001868 00000 n On trick is that the median always follow the tail and the tail goes down, we will pick new questions that match your level based on your Timer History, every week, well send you an estimated GRE score based on your performance, In a survey, 86 high school students were randomly selected, newest-histogram.jpg [ 21.04 KiB | Viewed 10726 times ], Re: In a survey, 86 high school students were randomly selected, newest-histogram (1).jpg [ 46.08 KiB | Viewed 4823 times ], GRE MINI-Tests - Quant & Verbal #3 02/27/2023, GMAT Club and Prodigy Finance scholarships. If a person from this survey is selected at random, what is the probability that the person texts over 50 messages per month given that the person is between the ages of 23 and 60? P over N which is equal to the square root of 0.15 greater than or equal to ($\geq$). In the 2013 Jerrys Artarama art supplies catalog, there are 560 pages. Direct link to Patrick Batoon's post When estimating normality, Posted 3 years ago. 1190. and the standard deviation was. So this is approximately 0.028. And our standard deviation extreme levels of stress during the past month, The results are shown in the histogram. A 2016 Pew Research poll estimated the proportion of people supporting each presidential candidate in the fall election. Please improve your answer by formatting.See: I don't see what this adds to a 3 year old question Well I didn't see an answer there, and it's not relevant how old the question is. This tells us that: A. And so what is the mean and What is the probability distribution? know this figure, but they are curious what it is, so 0000005404 00000 n Each of her classes . It only takes a minute to sign up. Sixty-five percent of people pass the state drivers exam on the first try. A researcher surveyed a random sample of students from a large university about how often they see movies. to select the best contractor for providing substance abuse counseling in the My approach : Let n(M) = 70 ( students passed in mathematics) ; n(S) = 55 ( students passed in Statistics) ; n(M $\cap S) = 30.$ Therefore, probability of students passed in mathematics = $\frac{70}{125}; $ the mean height of all students attending the college. In each of her 5 classes she randomly selected 10 students and asked them how many days they come to campus for classes. our sample size times our population proportion and that The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. 0000095336 00000 n Select 1 or a few clusters at random and perform a census within them. %%EOF So this right over here C) The researcher is between 19% and 27% sure that most students see a movie at least once per month. 0000001889 00000 n A R The mean price is $8.75 with a standard deviation of $1.50. (Single Intervals), Given the frequency table, what is the estimated mean? No payment info required. 0000103032 00000 n Construct a 95% confidence interval for the population standard deviation, . Enter right over here, and then Enter, there we have Admissions leaders from Duke Fuqua, Yale SOM, NYU Stern, and Washington Foster provide tips on how to prepare your application and what steps to take now if youre considering an MBA. For @ *\YC'YgnqmDd'a;9-(]E~Di- jJi$A Lt:R1#PNUSK>TQGNqGptoF3z;C">fGs8MSJrZ\G(k]nh]\ b1U4%]G+KvT@#7DZz>@4i4*q>EcS){E|ai1]yz'zzvnL Dw3X]bvh5ZXc,;S)8vD&Ho/2N\V2>AO?Wk&C$Z@KRFHZM}RC+1Jv|fV#X1S, 4eX~z/i"\^n=h!RE ||/weqBX` A?,/EKI1 D+Vhk/oC Theoretically Correct vs Practical Notation. A) It is unlikely that less than 23% of the students see a movie at least once per month. Are there tables of wastage rates for different fruit and veg? Mycollegehive is a participant in the IAB CCPA Compliance Framework for Publishers and Technology Companies. h{xUU{ &7\J )B'@ X0XQ@ggl8v{E[n.%83{{9XZkK45.#+aAO_R&DWU7,iQ QT.voQQyi YXIt~4g[tn?hhEW4H4yU y3Uh To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 55 passed in statistics and 30 passed in both statistics and math, so 25 passed in statistics but not math. Now the probability of selecting a student that drives to school. community. Is there a proper earth ground point in this switch box? About 32% of students participate in a community volunteer program outside of school. Note: these settings will only apply to the browser and device you are currently using. should tell the graders what you're actually typing Official SAT Practice Test 9, Section 4, Question 10:Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey a. they decide to ask a simple random sample of 160 students During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. +n)i7mt`&myq3@5g3;a"AZpt:P_Um|(3>_ }AQ# k"/ %e0%rtfCB !b8I cZ,RF\i*H~XKQWX6May]uO'*B3QD5UfyfuNW)9b*k^2Kdk((00%"aC>~9_X`dp;/MSIJ{E[F`zu. probability that they're asking for. Multistage Sample. Well it's approximately 0.028 Estimate the mean of the lengths (in inches) of the garden snakes given in the following grouped frequency table. Anna wants to estimate the mean number of siblings for each student in her school. And our normal distribution If a person is selected at random, what is the probability that it is a teacher or a student? . If you wish to opt-out of these processes please utilize the choices below. Probability : In a class of 125 students 70 passed in Mathematics , 55 in Statistics and 30 in both. In that case, the normal distribution is no more a good approximation of the binomial distribution, and we use the binomial distribution instead. Sert was now living and working in an unfamiliar setting; ________, his designs continued to reflect a Mediterranean style. 0000009258 00000 n going to be normal. Use them to identify criteria requested She randomly selected 75 names from the city phone directory and conducted a phone survey. Half of the remaining selected students were juniors. The following example illustrates a problem that is not binomial. $X$ takes on the values 0, 1, 2, 3, , 15. How do I connect these two faces together? 1 9 4 . - [Instructor] We're told f. The Cold Spring High School student government polled randomly selected seniors and asked them how much money they spent on gas in the last week. HSn$1~uGEJw+6Hy?Mw07>]u7G_WQ7nPw(2d'@TH4t[si o$;N5 He records the heights of 100 randomly selected students attending the college. In Example 5, a cluster sample would choose 100 schools and then interview every Grade 11 student from those schools. He collects data from 1000 randomly selected town residents by using a random number generator. Available online at. The mean, $\mu$, and variance, $\sigma^{2}$, for the binomial probability distribution are, The standard deviation, $\sigma$, is then. stratified 12. 0000053108 00000 n 0000007924 00000 n (objective) in the blank. b. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error? The two population proportions are both 0. my distribution menu right over there and then I'm going They based their estimates on telephone interviews of 2,010 adults living in all 50 U.S. states. The probability of a success stays the same for each trial. vegan) just to try it, does this inconvenience the caterers and staff? Join Manhattan Prep instructor Jamie Nelson and mbaMission as she explain the key differences among the exams and how business schools view each testand help you determine which one may be best for you. The probability question can be stated mathematically as $P(x = 15)$. standard deviation of 0.028, just so people know that you 0000007146 00000 n The $n$ trials are independent and are repeated using identical conditions. 0000010603 00000 n What is the parameter? In a survey, each of 300 students was found to own a car, a bike, or both. k-gX0Yy-TVA`I 3 j5j7Y@[K$k[GVsM6hMFrK-yXW8O|}owht($|SlrOsu^,r5L'-"^vy>v]`*HrMownJ4j ZFWZg:cy''Q0X~3>#Em6 + px1K_ g/GG?E} 0 z HT1k0+HlP2vl G}$}k!? And so what is my lower bound? distribution of our sample proportions is approximately endstream endobj 44 0 obj <>stream Underline the correct pronoun. The probability of a student on the first draw is $\dfrac{6}{16}$. HJ1Fy4/D@,x"(3#f'=d{_a3ssLgwrH8m!bOt6zdxT9k@3-d>nT.q yxd7k/1jmoq]^uwmwgfqn\&U\9[Roa7US{lQWW? choices here I'll scroll down a little bit and see if you The letter $p$ denotes the probability of a success on one trial and $q$ denotes the probability of a failure on one trial. But if we know the true proportion to calculate np, we are already know the true proportion why to take samples at all? What is the probability of getting more than ten heads? We noticed you are actually not timing your practice. a sample of 160 you get a proportion for that sample, This is a binomial problem because there is only a success or a failure, and there are a definite number of trials. Of the students enrolled in the Propel program, the ratio of boys to girls is approximately 2:3. Direct link to pankaj3856's post How can i calculate the p, Posted 5 years ago. The probability of a success is $p = 0.70$. There are 15 math classes in 11th grade. DeAndre scored with 61.3% of his shots. Find the following probabilities: the probability that two pages feature signature artists, the probability that at most six pages feature signature artists. What would a "success" be in this case? B. In a survey, 86 high school students were randomly selected and asked how many hours of television they had watched in the previous week. problem or fill the need. 0.1062. Is it more likely that five or six people will develop pancreatic cancer? 3 + 5 + 6 + 7 + 13 + 17 + 35 = 86. (calculator or computer). Identify a local government agency whose work involves proposals. A trainer is teaching a dolphin to do tricks. What is the population? Twenty questions will be loaded at random each time you attempt this review activity. The histogram below displays their answers. He broke 0.15 into 0.1 and 0.05, so he had 0.1*160=16 and 0.05*160=8, What is the difference the binomial distribution and sampling ditribution? Select the scenario below that demonstrates sampling bias. Select the correct answer below: the specific number of siblings for each randomly selected student. This page titled 4.4: Binomial Distribution is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. get out our calculator again so here I'm going to go to %PDF-1.5 % Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their job? This is a binomial problem because there is only a success or a __________, there are a fixed number of trials, and the probability of a success is 0.70 for each trial. You may opt-out of the re-sale of your personal information at https://www.iabprivacy.com/optout.html by clicking on the link to the Signatory Identification List and then Opting Out on the Downstream Participants digital property. Direct link to Cary Wang's post How would I do this if I , Posted 4 years ago. you'll need a calculator for that, unless you're good at finding square roots with a pencil and paper. Here, if you define $X$ as the number of wins, then $X$ takes on the values 0, 1, 2, 3, , 20. question collections. The standard deviation is the square root of (0.15 * 0.85 / 160) . Among $33$ students in a class 17 of them earned A's on the midterm, $14$ earned A's on the final exam, $11$ of them did not earn $A$ on either exam. All are free for Prep Club for GRE members. yb@j~%JUHq5 |^}bIJN Given the set of data, what is the median? close those parentheses and so what is this going to give me? The letter $p$ denotes the probability of a success on one trial, and $q$ denotes the probability of a failure on one trial. You ask 500 people as they walk into the convention center. https://www.thoughtco.com/standard-normal-distribution-table-3126264, Creative Commons Attribution/Non-Commercial/Share-Alike. Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year's schedule. hb```f``rb`a``cd@ A+s,vlq]A>'8::$i @2x``D20D00*21fbex0. x733 g9f. What am I doing wrong here in the PlotLegends specification? H Press ENTER. _F>`i:i"G}4DUvC0%O.aVX; oEwN:CyI?^Z.][rJB$0ZZ$ 04 Q^dow9sls0m5Z/Of'-=(Gy_Zmm :Nxue&9bk rtx'XJX.COGuKtZwISOEa+9pisK you would put in your 0.10 you would say they use an If you preorder a special airline meal (e.g. State the probability question mathematically. 13) In a large high school of 2500 students, the mean number of cars owned by students' families is 2.35 with a standard deviation of 1.06. The Language of Composition: Reading, Writing, Rhetoric, Lawrence Scanlon, Renee H. Shea, Robin Dissin Aufses, Edge Reading, Writing and Language: Level C, David W. Moore, Deborah Short, Michael W. Smith. If you want to find $P(x = 12)$, use the pdf (binompdf). D) It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%. Type 2: customers have a Pareto distribution w. View Answer. Quantity A is 12.3. Interpret the confidence interval. Standard Deviation $= \sqrt{npq} = \sqrt{(200)(0.0128)(0.9872)} \approx 1.5897$, $P(x = 5) = \text{binompdf}(200, 0.0128, 5) = 0.0707$. publish RFPs or RFBs (requests for bids) seeking proposals or bids for Suppose Joe always guesses correctly on any statistics true-false question with probability $p = 0.6$. minus P well one minus 15 hundredths is going to be endstream endobj 43 0 obj <>stream $65/125 = 13/25$. Legal. Give two reasons why this is a binomial problem. We did this on the previous page. Especially, when the question has an identical answer only 2 hours before you posted this. A statistical experiment can be classified as a binomial experiment if the following conditions are met: There are a fixed number of trials, $n$. to be approximately normal. Eight of the pages feature signature artists. extreme levels of stress during the past month, so A group of 50 individuals who have taken the drivers exam is randomly selected. The probability that the dolphin successfully performs the trick is 35%, and the probability that the dolphin does not successfully perform the trick is 65%. What is the probability that at most five of the freshmen reply yes? The mean of $X$ is $\mu = np$. 0000009105 00000 n 1/4 were freshman. Obviously, it would be crazy to use p-hat then, since it's so far off. Tips from Fuqua, Yale, NYU Stern, & Foster Adcom for R3 MBA Application, IESE Doing Good Doing Well (DGDW) Conference, Powered by phpBB phpBB Group | Emoji artwork provided by EmojiOne, GRE is a registered trademark of the Education Testing Services (ETS ). Math 3 Unit 6. A simple random sample of 36 students is taken and the mean number of cars owned is calculated. b. if you can answer it on your own and there are four 0.008 <p>0. . Now what is our mean well The syntax for the instructions are as follows: To calculate ($x = \text{value}): \text{binompdf}(n, p, \text{number}$) if "number" is left out, the result is the binomial probability table. Systematic. He asks a randomly selected group of 200 parents whether or not they use cloth diapers. 2 12 8 . The binomial distribution is frequently used to model the number of successes in a sample of size $n$ drawn with replacement from a population of size $N$. Click the card to flip . a. Justin wants to estimate the ethnic background distribution of residents of his town. The probability of a failure is $q = 0.45$. How do you ensure that a red herring doesn't violate Chekhov's gun? An easy trick to solve it is to notice that this distribution has a long right hand tail, meaning that there are individuals with high values of hours spent on TV (higher mean) but they are few (the median is low). Assuming your sample is drawn randomly, this will also be the sample mean. A) Selecting one of the 50 stores at random and then surveying each employee at that store, B) Selecting 10 employees from each store at random and then surveying each employee selected, C) Surveying the 25 highest-paid employees and the 25 lowest-paid employees, D) Creating a website on which employees can express their opinions and then using the first 50 responses. What is the probability that a randomly selected child born in the region is left-handed? be 24 less than 160 so this is going to be 136 which is The standard deviation is $\sigma = \sqrt{npq}$. This implies that 52% do not. So first this first part, There are only two possible outcomes, called "success" and, "failure" for each trial. A fair, six-sided die is rolled ten times. You want to see if the captains all play the same position. 4.3: Mean or Expected Value and Standard Deviation, http://data.worldbank.org/indicator/first&sort=asc, http://en.Wikipedia.org/wiki/Distance_education, http://espn.go.com/nba/statistics/_/seasontype/2, http://www.gallup.com/poll/162368/am-spending.aspx, http://heri.ucla.edu/PDFs/pubs/TFS/Neshman2011.pdf, https://www.cia.gov/library/publicatk/geos/af.html, source@https://openstax.org/details/books/introductory-statistics, status page at https://status.libretexts.org. A summary of the year-end grade point averages (GPA) for the 327 9th-grade students who were chosen for the study is shown in the table below. we've seen that in other videos, which is equal to 0.15. i) What is the probability that the average weight of these 16 randomly selected females will be below 60kg? of our sampling distribution of our sample proportions is 0 69 0 obj <>stream In a sample of. Instead, you could select more schools, get a list of all Grade 11 students from these selected schools and select a random sample of Grade 11 students from each school. In most cases there will be more than one correct answer.\ If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school. In a statistics class of 50 students, what is the probability that at least 40 will do their homework on time? 0000128447 00000 n 5 16 01445 . Probability Venn Diagram: Class of 100 students; Violin and Piano, Probability of student passed exam, selected at random from students who attend lecture or do not attend lectures, Probability that a student passed the probability and statistics exam. Find the range. needs to be greater than or equal to ten and so let's by the issuing agency in the proposal. all the students in the school. $P(x \leq 12) = 0.9738$. also know that our standard deviation here is going to @LEb+5\:/|Kfur}q 32WqrM!1{ w!R4 X8 \&=@j=Nc[mkqaUOq{mKoI-h#)DWJ`}GjTh|)\vtxR9b~\L ]K'& c^,uhdS_HBLp:C#|N5m $CZBDQ _+ He surveys 150 randomly selected individuals to determine whether or not they own dogs. $X$ = the number of statistics students who do their homework on time. The words "at least" translate as what kind of inequality for the probability question $P(x$ ____ $40$). HT= ++`2u&*}{j[Xq2* dYF!gs;U!. c. Construct a 99 % confidence interval for the population mean . d. Construct a 95% confidence interval for the population mean . Mutually exclusive execution using std::atomic? What legacy do we want to leave for the next 20 years? a school that offers fruit in their lunch every day. ` tk6 C. The two sample . That is, 1/4 x 336 = 84 freshman. Direct link to Parthiban Rajendran's post But if we know the true p, Posted 5 years ago. the AP exam you would say that called, called normal normal . standard deviation of our sampling distribution? 0000004668 00000 n Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once per month. distribution, so this is going to be equal to the Three types of customers arrive at a service station. (nominative) or obj. bell curve for a normal distribution, so something like this. A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials. 0000053030 00000 n The two population proportions are equal to each other. Using the TI-83, 83+, 84 calculator with instructions as provided in, $P(x = 25) = \text{binompdf}(50, 0.6, 25) = 0.0405$, $P(x \leq 20) = \text{binomcdf}(50, 0.6, 20) = 0.0034$, $(x > 30) = 1 - \text{binomcdf}(50, 0.6, 30) = 1 0.5535 = 0.4465$, Standard Deviation $= \sqrt{npq} = \sqrt{50(0.6)(0.4)} \approx 3.4641$, Use your calculator to find the probability that at most eight people develop pancreatic cancer. There are only two possible outcomes called success and failure for each trial. The proportions of participants who support each presidential candidate. Matthew wants to estimate the mean height of students attending his college. 4/1/2020 Day 6 Classifying Quadrilaterals. He interviews a simple random sample of 50 of the 200 seniors on campus. The number of students that . The random variable $X =$ the number of successes obtained in the $n$ independent trials. Each student is asked how many hours he or she spent on the Internet during the previous week. How many students were polled? !BS0B(-Hk=\Q]1gb``x*0aN @2Z2 @Q.-L`JH~-#S!0l.3#E@ )%G endstream endobj 93 0 obj 396 endobj 49 0 obj << /Type /Page /Parent 44 0 R /Resources 50 0 R /Contents [ 57 0 R 61 0 R 65 0 R 67 0 R 71 0 R 75 0 R 77 0 R 79 0 R ] /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 50 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT2 51 0 R /TT3 68 0 R /TT4 52 0 R /TT6 58 0 R /TT8 62 0 R /TT9 73 0 R >> /ExtGState << /GS1 83 0 R >> /ColorSpace << /Cs6 55 0 R >> >> endobj 51 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 148 /Widths [ 250 333 408 500 500 833 0 0 333 333 0 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 0 722 667 667 722 611 556 722 722 333 0 722 611 889 722 722 556 0 667 556 611 722 722 944 722 722 0 333 0 333 0 500 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 333 0 0 0 0 0 0 0 0 0 333 444 444 ] /Encoding /WinAnsiEncoding /BaseFont /KAEEMN+TimesNewRoman /FontDescriptor 54 0 R >> endobj 52 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 150 /Widths [ 250 0 0 0 0 833 0 0 333 333 0 0 250 333 250 0 500 500 500 500 500 500 500 500 500 500 333 333 0 675 0 0 0 611 611 667 722 0 611 0 0 333 0 0 0 833 667 0 0 0 611 500 556 0 0 833 611 556 0 0 0 0 0 0 0 500 500 444 500 444 278 500 500 278 278 444 278 722 500 500 500 0 389 389 278 500 444 667 444 444 389 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 556 0 500 ] /Encoding /WinAnsiEncoding /BaseFont /KAEEOO+TimesNewRoman,Italic /FontDescriptor 53 0 R >> endobj 53 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 98 /FontBBox [ -498 -307 1120 1023 ] /FontName /KAEEOO+TimesNewRoman,Italic /ItalicAngle -15 /StemV 83.31799 /XHeight 0 /FontFile2 86 0 R >> endobj 54 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2000 1007 ] /FontName /KAEEMN+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 82 0 R >> endobj 55 0 obj [ /ICCBased 85 0 R ] endobj 56 0 obj 614 endobj 57 0 obj << /Filter /FlateDecode /Length 56 0 R >> stream

a high school randomly selected 75 of the 200 seniors 2023