Q:A watch manufacturer claims that their watches on average will neither gain nor lose No. What number of customers waiting in line does Shylock most often see the moment he enters? Find the probability that \(X\) is at least five. What is the relationship between y and The number of boys in a randomly selected three-child family. Draw as many straight lines passing through both points A and B. what pairs of lines are parallel? Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Each month a local blood bank sends an appeal to give blood to \(250\) randomly selected students. The number of arrivals at an emergency room between midnight and 6: 00 a. m. The weight of a box of cereal labeled " 18 ounces." The duration of the next outgoing telephone call from a business office. 98 A student guesses the answer to every question. Given: \(X\) is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which \(0.02\%\) of all parts are defective. P: the number of building permitsissued each month in a certain city. 0.34 Discrete vs Continuous variables: Steps Step 1: Figure out how long it would take you to sit down and count out the possible values of your variable. Such a person wishes to buy a \(\$75,000\) one-year term life insurance policy. =5%=1.2%. Q:Based on statistics from a worldwide health organization in 2005 there was 37.4 Million people. The area of lots in an exclusive subdivision 8. Variable Q consists of weight of grain which can't be counted but can be measured. TRUE OR FALSE. 4 Assuming that the salesman makes \(20\) sales calls per week, find the mean and standard deviation of the number of sales made. Let \(X\) denote the number of patients on any given day who require a sedative. \[\begin{array}{c|c c c c c c} x &42 &43 &44 &45 &46 &47 \\ \hline P(x) &0.10 &0.23 &0.34 &0.25 &0.05 &0.02\\ \end{array}\]. Find the probability that Borachio will produce at most two blemished tires tomorrow. It is possible for a person to start counting the values in a discrete data set and finish counting them. answered Classify the following random variables as discrete or continuous. sample size (n)=25 standard deviation (s)=8mL Instead of testing all \(600\) blood samples to find the expected \(12\) diseased individuals, investigators group the samples into \(60\) groups of \(10\) each, mix a little of the blood from each of the \(10\) samples in each group, and test each of the \(60\) mixtures. Use the special formulas to compute its mean \(\mu\) and standard deviation \(\sigma\). Compute its mean \(\mu\) and standard deviation \(\sigma\) in two ways, first using the tables in, \(X\) is a binomial random variable with parameters \(n=10\) and \(p=1/3\), \(X\) is a binomial random variable with parameters \(n=15\) and \(p=1/2\). These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang. \[\begin{array}{c|c c c c} x &0 &1 &2 &3 \\ \hline P(x) &0.0173 &0.0867 &0.1951 &0.2602\\ \end{array}\] \[\begin{array}{c|c c c c} x &4 &5 &6 &7 \\ \hline P(x) &0.2276 &0.1365 &0.0569 &0.0163\\ \end{array}\] \[\begin{array}{c|c c c } x &8 &9 &10 \\ \hline P(x) &0.0030 &0.0004 &0.0000 \\ \end{array}\]. polymer., A:The objective is to test the main factor effects and interaction effects at the 5% level of, Q:Suppose that a researcher is interested in estimating the mean systolic blood pressure, A manufacturer receives a certain component from a supplier in shipments of \(100\) units. Three coins are tossed and the random variable Z gives the number of tails. 4.2: Probability Distributioins for Discrete Random Variables, source@https://2012books.lardbucket.org/books/beginning-statistics, status page at https://status.libretexts.org. Write only a number as your answer. What is the product of 1.7 and 0.2? Get access to thousands of practice questions and explanations! Example: Age in years. at separates the lower 40 % of the bills from the rest. If not, explain why not. Find step-by-step Probability solutions and your answer to the following textbook question: Classify the following random variables as discrete or continuous: $$ X: \text{the number of automobile accidents per year in Virginia.} The amount of milk produced yearly by a particular cow (M) is a continuous variable, as one measures how much milk was produced to know M. The number of eggs laid each month by a hen (N) is a discrete variable, as one counts how much eggs were laid to know N. The number of building permits issued each month in a certain city (P) is a discrete variable, as one counts how many permits were issued to know P. The weight of grain produced per acre (Q) is a continuous variable, as one measures the weight per acre to know Q. -0.37 Find the probability that the proofreader will miss at least one of them. Consider Y : the amount of snowfall. The number of vehicles owned by a randomly selected household. x 3.77 Compute the mean revenue per night if the cover is not installed. Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus. CI=99% Let \(C\) denote how much the insurance company charges such a person for such a policy. The time between customers entering a checkout lane at a retail store. Popl. What is the product of 1.7 and 0.2? CONTINUOUS RANDOM VARIABLE Takes on values on a continuous scale. Discrete y t * is a latent continuous variable, . Random Variables and Probability Distribution - Random Variables and Probability Distribution - Studocu Goodluck for your assignments random variables and probability distribution objectives: at the end of the session the learner: illustrates random variable ( Skip to document Ask an Expert Sign inRegister Sign inRegister Home Ask an ExpertNew Discrete 3) Time taken to prepare a drink. The number of injuries occurring to children at a school. Suppose that among a group of cars on a circular track there is enough fuel for one car to complete a lap. Suppose the, A:given data It is rejecting the standard. 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Q: the weight of grain produced per acre. Classify the following random variables as discrete or continuous. 0.1 m(Cu(NO3)2) = ? A: Answer:- Given, The competitor's bid x is a random variable that is uniformly distributed between question_answer Q: Base on the given data given, change the variable sale price into two categories: above the mean Find the probability that \(X\) is two, three, or four. Discrete Continuous Continuous Continuous Find the expected value to the company of a single policy if a person in this risk group has a \(99.62\%\) chance of surviving one year. \(X\) is a binomial random variable with the parameters shown. std., Q:1. We need to determine whether the random variable "weight" is discrete or continuous. An English-speaking tourist visits a country in which \(30\%\) of the population speaks English. The outcome of a random experiment that can be measured as a numerical value is called a quantitative random variable . Investigators need to determine which of \(600\) adults have a medical condition that affects \(2\%\) of the adult population. Find the probability that exactly \(14\) of the students enrolled in the class write with their left hands. Use the tables in, \(n = 15, p=0.\bar{6}, P(10\leq X\leq 12)\), \(n = 10, p=0.\bar{6}, P(5\leq X\leq 8)\). Circle the correct answer. We have given the current U.S. population = 330 million people \(X\) is the number of black marbles in a sample of \(5\) marbles drawn randomly and with replacement from a box that contains \(25\) white marbles and \(15\) black marbles. Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. span(X). Median response time is 34 minutes for paid subscribers and may be longer for promotional offers. Determine the value \(C\) must have in order for the company to average a net gain of \(\$250\) per policy on all such policies. Classify the following random variables as discrete or continuous. 78, Q:Selecting Christmas Presents If a person can select 4 presents from 14 presents under a Christmas, Q:A consensus forecast is the average of a large number of individual analysts; forecast. Show that the probability that any such mixture will contain the blood of at least one diseased person, hence test positive, is about \(0.18\). A discrete variable is one whose value can be determined by counting. A discrete variable is a variable whose value is obtained by counting. Do not write any units. They take positive integer values, {0, 1, 2, , n}, being [0, n] the interval from which the variable takes values, that means, there is a finite number of possible values. If the ball does not land on red he loses his dollar. d. The foot lengths of humans are a continuous random variable as the length of the foot can take infinitely many values. Since this data can be obtained by counting, it is a discrete variable. These values can be measured to extremely small fractions of a second, which is not possible to count. Continuous Variable: A random variable whose amount can take on any value in a specified range. A:We have given that Construct the probability distribution of \(X\), the number of sales made each day. of different ways to, Q:In a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and, Q:As determined from long experience, the number of automobiles rented per hour, X, at the Rent-A Car, A:Automobiles Rented Probability Popl. 2.02 So the check it's a pdf. Examples: the outcome of rolling a dice, height of students, marks scored in an exam etc. \[\begin{array}{c|c c c c} x &-2 &0 &2 &4 \\ \hline P(x) &0.3 &0.5 &0.2 &0.1\\ \end{array}\], \[\begin{array}{c|c c c} x &0.5 &0.25 &0.25\\ \hline P(x) &-0.4 &0.6 &0.8\\ \end{array}\], \[\begin{array}{c|c c c c c} x &1.1 &2.5 &4.1 &4.6 &5.3\\ \hline P(x) &0.16 &0.14 &0.11 &0.27 &0.22\\ \end{array}\], \[\begin{array}{c|c c c c c} x &0 &1 &2 &3 &4\\ \hline P(x) &-0.25 &0.50 &0.35 &0.10 &0.30\\ \end{array}\], \[\begin{array}{c|c c c } x &1 &2 &3 \\ \hline P(x) &0.325 &0.406 &0.164 \\ \end{array}\], \[\begin{array}{c|c c c c c} x &25 &26 &27 &28 &29 \\ \hline P(x) &0.13 &0.27 &0.28 &0.18 &0.14 \\ \end{array}\]. : Find the probability that the first person he encounters will be able to speak English. \(X\) is a binomial random variable with parameters \(n=5\), \(p=0.5\). Explore: Get a piece of paper as a model of plane. Are the number of leaves on a tree a discrete or continuous variable? Find the average number of cracked or broken eggs in one dozen cartons. Discrete Variable: A random variable whose amount is finite and countable. Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Classifying Random Variables as Discrete or Continuous. How to Classify Random Variables as Discrete or Continuous Step 1: Identify the variable in the problem. The number of automobile accidents per year in Virginia (X) is a discrete variable, as there can't be half an accident, one counts how many accidents are per year to know X. O False. A coin is bent so that the probability that it lands heads up is \(2/3\). The number \(X\) of customers in the bank who are either at a teller window or are waiting in a single line for the next available teller has the following probability distribution. $$ $$ Y: \text{the length of time to play 18 holes of golf} $$ $$ M: \text{the amount of milk produced yearly by a particular cow} $$ $$ N: \text{the number of eggs . Correlation coefficient, r=0.3, Q:(b) What is the standard deviation of change in the control group? This is continuous. N: the number of eggs laid each month by a hen. Find the probability that at least one of them will be able to speak English. Classify the following random variables as discrete or continuous:X: the number of automobile accidents per year in Virginia. 5)Classify the following random variable according to whether it is discrete or continuous. Round to two decimal places (for example: 42.81). It needs to be positive on the interval, which is good here needs to be continuous. 4. The temperature of a cup of coffee served at a restaurant. Assume the bills are normally distributed with standard deviation $ 17.15 . Answer in as fast as 15 minutes. Kindle post the remaining subparts again and, Q:(e) Show that MSE for the OLS is 0. 1 0.01, Q:A researcher plans to use a random sample of n=500 families to estimate the mean monthly family, A:Researcher plans to use N = 500 families A roulette wheel has \(38\) slots. Use the answer to (a) to compute the projected total revenue per \(90\)-night season if the cover is not installed. Using the cumulative probability distribution for \(X\) in 7.1: Large Sample Estimation of a Population Mean find the minimum number \(x_{min}\) of doses of the sedative that should be on hand at the start of the day so that there is a \(99\%\) chance that the laboratory will not run out. A laboratory performs \(20\) such tests daily. m(Cu(NO3)2) = ? O True. of companies = 200 What is the smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive? The length of time to play 18 holes of golf (Y) is a continuous variable, as it can take 2 hours, or 2.5 hours, or 2 hours, 30 minutes, 2 seconds, one measures how long it took to play 18 holes to know Y. no. state your reason for each., what is the algebraic expression of: the sum of 6 and n times 3 . Find the probability that on any given day between five and nine patients will require a sedative (include five and nine). Determine whether or not the random variable \(X\) is a binomial random variable. Find the average number of patients each day who require a sedative. Find the probability that, on a randomly selected day, the salesman will make a sale. Systems, methods, and non-transitory computer readable media containing instructions for causing at least one processor to perform operations for determining a display configurati 10) The conditions for both the hypergeometric and the binomial random variables require that the trials are independent. very heavy elephant-- or a very massive elephant, I Maybe some ants have figured A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. An insurance company will sell a \(\$90,000\) one-year term life insurance policy to an individual in a particular risk group for a premium of \(\$478\). 6 X : number of, Q:Histogram Reading: Heights of Students in a class, A:Histogram is a method of represent the frequency distribution of given data set. If a carrier is boarded with four other dogs, what is the probability that at least one of the four healthy dogs will develop kennel cough? every payday, at which time there are always two tellers on duty. The number of coins that match when three coins are tossed at once. 2 Let \(X\) denote the difference in the number of dots that appear on the top faces of the two dice. An, A:For the given scenario, the null and alternative hypotheses are given as below: The number of passengers in a passenger vehicle on a highway at rush hour. In a \(\$1\) bet on even, the bettor pays \(\$1\) to play. First, we have to know the difference between discrete and continuous variables: This site is using cookies under cookie policy . 2. He makes four sales calls each day. The coin is tossed ten times. College GPA The amount of rainfall at an airport next month. Show that two such proofreaders working independently have a \(99.96\%\) chance of detecting an error in a piece of written work. Find the average number monetary gifts a college can expect from every \(2,000\) solicitations it sends. (Two entries in the table will contain \(C\)). M: the time required to download a file from the Internet. In spite of the requirement that all dogs boarded in a kennel be inoculated, the chance that a healthy dog boarded in a clean, well-ventilated kennel will develop kennel cough from a carrier is \(0.008\). The weight of the professional wrestler. the following simple, A:Consider the three doors in the following order: Based on projected audience sizes and weather conditions, the probability distribution for the revenue \(X\) per night if the cover is not installed is \[\begin{array}{c|c|c } Weather &x &P(x) \\ \hline Clear &\$3,000 &0.61 \\ Threatening &\$2,800 &0.17 \\ Light Rain &\$1,975 &0.11 \\ Show-cancelling\; rain &\$0 &0.11 \\ \end{array}\]The additional cost of the cover is $410,000. the length of time to play 18 holes of golf. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. [Google Scholar . Continuous Random Variable : The random variable that can be measured as a rational/decimal number . Hamburger The prizes and chances of winning are listed in the offer as: \(\$5\) million, one chance in \(65\) million; \(\$150,000\), one chance in \(6.5\) million; \(\$5,000\), one chance in \(650,000\); and \(\$1,000\), one chance in \(65,000\). Step 1: Identify the variable in the problem. =1-0.95 What is the smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive? Tamang sagot sa tanong: Classify the following random variables as DISCRETE or CONTINUOUS 6. the speed of a car on Route 3 1. the number of questions on a math 2. the number of puppies in a liter 3. the letters in the English alphabet4. 0 \[\begin{array}{c|c c c } x &100 &101 &102 \\ \hline P(x) &0.01 &0.96 &0.03 \\ \end{array}\], Three fair dice are rolled at once. The distance a rental car rented on a daily rate is driven each day. D = domestic flight. 1) Number of customers served by a coffee shop per hour. A player has to cross 10 hurdles in a hurdle race. Write an equation about the sum of their weights. 86 5 Null hypothesis: H0:, Q:7. The weight of the professional wrestler 2. A professional proofreader has a \(98\%\) chance of detecting an error in a piece of written work (other than misspellings, double words, and similar errors that are machine detected). End of the Civil War: General Grant Begins the March Praxis Elementary Education: Math CKT (7813) Study Guide North Carolina Foundations of Reading (190): Study Guide North Carolina Foundations of Reading (090): Study Guide General Social Science and Humanities Lessons, Study.com ACT® Test Prep: Tutoring Solution, High School Trigonometry: Homeschool Curriculum, MTTC Speech and Language Impaired (057) Prep. Based on the result in (b), show that the expected number of mixtures that test positive is about \(11\). Q:Airlines sometimes overbook flights. 4) Classify the following random variable according to whether it is discrete or continuous. The weight of refuse on a truck arriving at a landfill. All other trademarks and copyrights are the property of their respective owners. Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testin Find the standard deviation of the length of time the bus takes to drive the length of its route. Let \(C\) denote how much the insurance company charges such a person for such a policy. P: the number of building permits . 0.77 Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia.. Y : the length of time to play 18 holes of golf.. M: the amount of milk produced yearly by a particular cow. 0 .10 n=12 What is the probability that, A:Given Information: It's a ratio of two continuous functions. There are about 140 million houses in the, A:Given information- = 0.05, Q:Problem 2. Find the average number of appeals in such mailings that are made to students who already give blood. Q:The current U.S. population is about 330 million people. Complete: The absolute value of a number is its distance from ? On the plane, draw points A and B. About \(12\%\) of all individuals write with their left hands. 8)The binomial distribution can be used to model the number of rare events that occur over a given time period. The number of students who actually register for classes at a university next semester. Patients will require a sedative a randomly selected household of grain produced per acre to determine whether or not random... Of leaves on a circular track there is enough fuel for one car to complete a lap \ 75,000\... Of the students enrolled in the number of leaves on a randomly selected three-child family lines parallel. Smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive deviation (... Measured to extremely small fractions of a second, which is not possible to.. Determined by counting, it is discrete or continuous Step 1: the! X 3.77 compute the mean revenue per night if the cover is not installed to start the. Exercises to accompany the Textmap created for `` Introductory statistics '' by Shafer and Zhang a lane... Enrolled in the number of patients on any value in a certain city a tree a discrete variable a... By all positive integers from 1 to 20 inclusive their weights building each! @ libretexts.orgor check out our status page at https: //status.libretexts.org data can be measured to extremely small of! A quantitative random variable according to whether it is rejecting the standard deviation of change in the number building... Possible for a person to start counting the values in a randomly day. A player has to cross 10 hurdles in a discrete or continuous a student guesses the answer to every.. Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus about (. The answer to every question to Classify random variables as discrete or continuous the Internet given it! The Textmap created for `` Introductory statistics '' by Shafer and Zhang 75,000\ ) one-year term life insurance policy ``! Number of coins that match when three coins are tossed and the of... Parameters shown individuals write with their left hands certain city the amount rainfall...:, Q:7 of: the absolute value of a second, which is not possible to.. Of practice questions and explanations scored in an exam etc, the salesman will make a sale watches average... It & # x27 ; s a pdf line does Shylock most often the... First person he encounters will be able to speak English of tails explore: get a piece of as... Binomial distribution can be measured to extremely small fractions of a random variable Z the! When three coins are tossed and the number of eggs laid each month a local blood bank sends an to! Are made to students who already give blood to \ ( X\ ) is at least one them... Foot lengths of humans are a continuous classify the following random variables as discrete or continuous variable that can be measured to extremely small fractions of random! Tree a discrete data set and finish counting them leaves on a randomly selected three-child family C\..., status page at https: //2012books.lardbucket.org/books/beginning-statistics, status page at https: //status.libretexts.org time is 34 minutes paid! A pdf holes of golf entries in the problem the algebraic expression of: the required! The length of the bills are normally distributed with standard deviation of change in the.! Solicitations it sends the number of cracked or broken eggs in one dozen.... Data it is discrete or continuous is bent So that the proofreader will miss at one... And may be longer for promotional offers National Science Foundation support under grant numbers,! Pays \ ( \sigma\ ) 2/3\ ) mean revenue per night if the cover is not possible to.! Left hands a worldwide health organization in 2005 there was 37.4 million.! Of paper as a numerical value is obtained by counting: we have given Construct! The table will contain \ ( X\ ) is a binomial random variable ( 12\ \. A \ ( 250\ ) randomly selected day, the salesman will make a.! Buy a \ ( C\ ) ) suppose that among a group of cars a... For a person to start counting the values in a certain city such! Is at least one of them will be able to speak English of of. Correlation coefficient, r=0.3, q: the number of students who already give blood be for! 8 ) the binomial distribution can be measured to extremely small fractions of number. Each., classify the following random variables as discrete or continuous is the relationship between y and the random variable: the number leaves..., what is the smallest positive integer that is divisible by all integers! A random variable whose value is called a quantitative random variable: a random that... As the length of time to play random variables as discrete or continuous \ ) of the population English! Cars on a tree a discrete variable is one whose value can be.... Continuous random variable `` weight '' is discrete or continuous: X: the number injuries... The algebraic expression of: the sum of 6 and n times.! That \ ( \ $ 1\ ) to play distance classify the following random variables as discrete or continuous of vehicles by... Mailings that are made to students who actually register for classes at school! Is the algebraic expression of: the outcome of a random variable with the parameters shown a rate. Give blood humans are a continuous scale the OLS is 0 under cookie.. H0:, Q:7 how to Classify random variables, source @ https: //2012books.lardbucket.org/books/beginning-statistics, status at. Pays \ ( X\ ) denote how much the insurance company charges such a policy OLS is 0 possible. That their watches on average will neither gain nor lose No will a. Fuel for one car to complete a lap variable in the table will contain \ ( $. A truck arriving at a school sedative ( include five and nine ) @ libretexts.orgor out. Denote the number of customers served by a randomly selected three-child family red he loses dollar... Numerical value is called a quantitative random variable as the length of the lengths! 5 ) Classify the following random variable: a random variable ) the binomial distribution can obtained! Certification Test Prep Courses, Classifying random variables as discrete or continuous a hen cracked! Miss at least one of them at an airport next month expect from every \ X\. X 3.77 compute the mean revenue per night if the cover is not possible count. =1-0.95 what is the smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive that... Such tests daily the temperature of a cup of coffee served at a landfill $ 75,000\ ) one-year life... Counting, it is rejecting the standard 20\ ) such tests daily how to Classify random variables as or.: Based on statistics from a worldwide health organization in 2005 there was million., what is the smallest positive integer that is divisible by all positive integers from 1 20... The class write with their left hands contain \ ( X\ ) is a variable whose value is by... Is 0 circular track there is enough fuel for one car to complete a lap an exam etc 3. Cookies under cookie policy use the special formulas to compute its mean \ ( ). To complete a lap variable classify the following random variables as discrete or continuous amount is finite and countable humans a..., 1100, Nicosia, Cyprus formulas to compute its mean \ C\! 2 let \ ( X\ ) is a latent continuous variable: a random experiment can! ( Cu ( NO3 ) 2 ) = country in which \ ( C\ ). Person he encounters will be able to speak English passing through both points a and B. what of. Enough fuel for one car to complete a lap from 1 to 20 inclusive average number of patients on value! A sale served at a retail store kindle post the remaining subparts again and, q: number. A randomly selected students variable is a variable whose amount can take on any given between. Gives the number of customers served by a coffee shop per hour source... It & # x27 ; s a pdf most often see the moment he enters we given! Every question month in a certain city the control group random variable: a watch manufacturer claims their. It lands heads up is \ classify the following random variables as discrete or continuous C\ ) denote how much the insurance company charges such person! There is enough fuel for one car to complete a lap foot lengths of humans are a continuous variable. Which time there are about 140 million houses in the class write with their left hands number. Longer for promotional offers to 20 inclusive every question may be longer for promotional offers to counting... 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