10) The conditions for both the hypergeometric and the binomial random variables require that the trials are independent. 1 This site is using cookies under cookie policy . Find the probability that the proofreader will miss at least one of them. Compute the mean revenue per night if the cover is not installed. Which of the following represents the critical region for this mentioned sample (MUST SHOW WORK, A:Answer:- Given, population mean, = 30 The weight of refuse on a truck arriving at a landfill. If the experiment of dropping the tack \(15\) times is done repeatedly, what is the average number of times it lands with its point in the air? Find the probability that Borachio will produce more than three blemished tires tomorrow. 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 number of arrivals at an emergency room between midnight and \(6:00\; a.m\). Find the standard deviation of the length of time the bus takes to drive the length of its route. Let \(X\) denote the net gain from the purchase of a randomly selected ticket. the length of time to play 18 holes of golf. Show that two such proofreaders working independently have a \(99.96\%\) chance of detecting an error in a piece of written work. Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. If so, give the values of \(n\) and\(p\). 2.39 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. The number of heads in two tosses of a coin. (Two entries in the table will contain \(C\)). 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. 2. weight of the newborns each year in a hospital 3. the number of siblings in a family of a region f 4. the speed of a car 5. the amount of sugar in a cup of coffee All other trademarks and copyrights are the property of their respective owners. In a hamster breeder's experience the number \(X\) of live pups in a litter of a female not over twelve months in age who has not borne a litter in the past six weeks has the probability distribution \[\begin{array}{c|c c c c c c c} x &3 &4 &5 &6 &7 &8 &9 \\ \hline P(x) &0.04 &0.10 &0.26 &0.31 &0.22 &0.05 &0.02\\ \end{array}\]. Use the formula for weighted data. 2010, 31, 2225-2236. 4) Classify the following random variable according to whether it is discrete or continuous. 6 Kelly Hawkins has taught high school math for over 5 years. 1) Number of customers served by a coffee shop per hour. Classify the following random variables as discrete or continuous. Enter the email address you signed up with and we'll email you a reset link. If it costs Tybalt \(44\) cents to mail his entry, what is the expected value of the sweepstakes to him? Let \(X\) denote the number of boys in a randomly selected three-child family. -0.47 3.21 Kindle post the remaining subparts again and, Q:(e) Show that MSE for the OLS is 0. Let our experts help you. The weight of the professional wrestler. The number of injuries occurring to children at a school. This is continuous. 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 \(p=1/2\). What is the smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive? The number of kernels of popcorn in a \(1\)-pound container. Thus for example if a one and a five are rolled, \(X=4\), and if two sixes are rolled, \(X=0\). Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Find the probability that \(X\) is at least five. Based on the, A:A scatter plot is a graphical representation of two variables to investigate if there exists an, Q:True or false. x The coin is tossed ten times. The number of deaths per year attributed to lung cancer. These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang. Step 1: Identify the variable in the problem. The time, to the nearest whole minute, that a city bus takes to go from one end of its route to the other has the probability distribution shown. Depending on the size of the school district, it might take a while to count, but the process would eventually end. Classify the following random variables as discrete or continuous. The independent variables are lagged, and are the following: Inflation stands for the next year's expected inflation rate minus 2% (Consensus Economics), . The number of clerical errors on a medical chart. span(X). The temperature of a cup of coffee served at a restaurant. O continuous . The probability that an egg in a retail package is cracked or broken is \(0.025\). Variable X consists of number of automobile accidents which can be counted. \ ( \mathrm {W}= \) the total surface area of a randomly selected person's body \ ( X= \) the quantity of oil in a randomly selected oil spill in the sea \ ( \mathrm {Y}= \) the quantity of pots in a randomly selected restaurant kitchen \ ( Z \) = the total cent value of Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. 3. infinitely uncountable number of potential values, regularly. Find the probability that the next litter will produce at least six live pups. (For fair dice this number is \(7\)). 92 The data is as follows: on a number line. Write only a number as your answer. the number of defective computers produced by a manufacturer. Discrete 3) Time taken to prepare a drink. Continuous at separates the lower 40 % of the bills from the rest. Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus. Classify the following random variables as discrete or continuous. (Enter != for as. 3.36. The number of accidents per year at an intersection. Recalculate according to your conditions! Construct the probability distribution for \(X\). Moment generating function of X is A. 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. The discrete random variable showing the policy rate adjustments for each country is denoted by y t. . Goneril buys ten skeins to crochet an afghan. What assumptions can you make out of this activity? \(X\) 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. One-third of all patients who undergo a non-invasive but unpleasant medical test require a sedative. 2.17 Questions The variable in the problem is the number of students in an entire school district. Many phenomena can be viewed as examples of a random walk. 3. Assume the bills are normally distributed with standard deviation $ 17.15 . Student Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus. -0.37 M: the amount of milk produced yearly by a particular cow.N: the number of eggs laid each month by a hen. 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. This page titled 4.E: Discrete Random Variables (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 54 He makes four sales calls each day. So, it is a continuous variable. Classify each random variable as either discrete or continuous. An insurance company will sell a \(\$10,000\) one-year term life insurance policy to an individual in a particular risk group for a premium of \(\$368\). Show that the probability that any such mixture will contain the blood of at least one diseased person, hence test positive, is about \(0.18\). Construct the probability distribution for the number \(X\) of defective units in such a sample. Find the expected value to the company of a single policy if a person in this risk group has a \(97.25\%\) chance of surviving one year. Q: the weight of grain produced per acre. Q:What is the standard deviation of this distribution? Q:The values of P(Z0.1) and P (Z0.1) are the same. [Google Scholar . Use the first variable for the x-axis. A) continuous B) discrete Click the card to flip Definition 1 / 10 B Click the card to flip Flashcards Learn Test Match Created by josymvelasquez Terms in this set (10) 1. C. 0.19 the number of eggs laid each month by a hen. Assume the bills are normally distributed with standard deviation $ 17.15 . In a certain board game a player's turn begins with three rolls of a pair of dice. Total no. The number of vehicles owned by a randomly selected household. The average amount spent on electricity each July by a randomly selected household in a certain state. Often, continuous random variables represent measured data, such as heights, weights, and temperatures. He needs to ask someone directions. \[\begin{array}{c|c c c } x &100 &101 &102 \\ \hline P(x) &0.01 &0.96 &0.03 \\ \end{array}\], Three fair dice are rolled at once. What is the product of 1.7 and 0.2? a. P(z -1.0) b. P(Z > -1.0) c. P(Z > -1.5) vising nurse wants to visit all patients in one day. 0 Are asked to verify that this is a pdf over this interval and then find the probability that the random variable is between two and 15. The average weight of newborn babies born in a particular county one month. The variable in the problem is the number of leaves on a tree. 8 The probability distribution for \(X\) is \[\begin{array}{c|c c c } x &0 &u &3 \\ \hline P(x) &p &\frac{15}{36} &\frac{1}{36} \\ \end{array}\]. Let \(X\) denote the number of times a fair coin lands heads in three tosses. Two fair dice are rolled at once. So, it is a discrete variable. The tourist sees four local people standing at a bus stop. The mean \(\mu\) of \(X\). \(X\) is a binomial random variable with parameters \(n=16\) and \(p=0.74\). Movie lengths are an uncountable set. Discrete 2) Amount of milk used per drink. \(X\) is the number of coins that match at least one other coin when four coins are tossed at once. A roulette wheel has \(38\) slots. Determine the value \(C\) must have in order for the company to break even on all such policies (that is, to average a net gain of zero per policy on such policies). 13. If you are given one trigonometric ratio for an acute angle in a right triangle, explain what steps are needed to find the other two trigonometric ratios. Quantitative Random Variables . Continuous Pizza Find the probability that \(X\) is two, three, or four. Each month a local blood bank sends an appeal to give blood to \(250\) randomly selected students. 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 \(\$478\). P: the number of building permits . Her sister weighs 12 pounds more. the number of building permits issued each month in a certain city. A. random variable B. variable C. probability D. probability distribution B. Classify the following random variables as discrete or continuous. What is the relationship between y and = 0.05, Q:Problem 2. A corporation has advertised heavily to try to insure that over half the adult population recognizes the brand name of its products. In a random sample of \(20\) adults, \(14\) recognized its brand name. Compute the probability indicated. Five thousand lottery tickets are sold for \(\$1\) each. Get access to millions of step-by-step textbook and homework solutions, Send experts your homework questions or start a chat with a tutor, Check for plagiarism and create citations in seconds, Get instant explanations to difficult math equations. 1.9 A fair coin is tossed repeatedly until either it lands heads or a total of five tosses have been made, whichever comes first. Classify the following random variables as discrete or continuous. no: the sum of the probabilities exceeds \(1\), no: the sum of the probabilities is less than \(1\), \[\begin{array}{c|c c c c} x &0 &1 &2 &3 \\ \hline P(x) &1/8 &3/8 &3/8 &1/8\\ \end{array}\], \[\begin{array}{c|c c c c} x &-1 &999 &499 &99 \\ \hline P(x) &\frac{4987}{5000} &\frac{1}{5000} &\frac{2}{5000} &\frac{10}{5000}\\ \end{array}\], \[\begin{array}{c|c c c } x &C &C &-150,000 \\ \hline P(x) &0.9825 & &0.0175 \\ \end{array}\], \[\begin{array}{c|c c } x &-1 &1 \\ \hline P(x) &\frac{20}{38} &\frac{18}{38} \\ \end{array}\], \[\begin{array}{c|c c c c c c} x &0 &1 &2 &3 &4 &5 \\ \hline P(x) &\frac{6}{36} &\frac{10}{36} &\frac{8}{36} &\frac{6}{36} &\frac{4}{36} &\frac{2}{36} \\ \end{array}\], \[\begin{array}{c|c c c } x &0 &1 &2 \\ \hline P(x) &0.902 &0.096 &0.002 \\ \end{array}\]. A roulette wheel has \(38\) slots. This site is using cookies under cookie policy . Find the expected number of skeins that contain knots. D = domestic flight. Your friend Caroline helped you with the null, A:Given that, O False. Math Statistics Topic: CENTRALIZATION AND DISPERSION MEASURES DISCRETE VARIABLE In a group of families considering the number of children, the following values have been obtained 2 0 2 4 4 6 6 4 6 7 4 4 7 4 2 0 4 6 7 7 A. [1 pt each] Time to finish a race d. Number of doubles in a roll of two dice 1 b. A discrete random variable \(X\) has the following probability distribution: \[\begin{array}{c|c c c c c} x &13 &18 &20 &24 &27 \\ \hline P(x) &0.22 &0.25 &0.20 &0.17 &0.16 \\ \end{array}\]Compute each of the following quantities. Geographic Interactions in Culture & the Environment, Geographic Diversity in Landscapes & Societies, Tools & Methodologies of Geographic Study, PLACE Mathematics: Solving Trigonometric Equations, Fundamental Values & Principles of Civil Society, ORELA Math: Discrete Probability Distributions, FTCE: Analyzing Data and Drawing Conclusions, Quiz & Worksheet - Complement Clause vs. T: 02743.899.588 - 0985.173.317 Ms Hng - 0908.131.884 Mr Quyn You can specify conditions of storing and accessing cookies in your browser, B Classify the following random variables as discrete or continuous, 1. the number of defective computers produced by a manufacturer. 4 (A tree diagram is helpful). Determine whether or not the random variable \(X\) is a binomial random variable. 1. . The number of pitches made by a starting pitcher in a major league baseball game. The % change is computed in terms of % increase and % decrease. You can specify conditions of storing and accessing cookies in your browser, 091236382866828589466929558292257394847392916739)1/19197363738949595729029283. 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. \(X\) is a binomial random variable with parameters \(n=5\), \(p=0.5\). Systems, methods, and non-transitory computer readable media containing instructions for causing at least one processor to perform operations for determining a display configurati \(X\) 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. The number of students who actually register for classes at a university next semester. The number of accident-free days in one month at a factory. Application 1. the number of defective computers produced by a manufacturer (10 mins.) Find the probability that on any given day between five and nine patients will require a sedative (include five and nine). The sum of their weights is 330 pounds. no. the number of . Construct the probability distribution of \(X\). Compute the mean and standard deviation of \(X\). 80 What Is Plantar Fasciitis? Draw as many straight lines passing through both points A and B. The amount of rainfall at an airport next month. Bills are normally distributed with standard deviation of this activity expected number of permits... Of doubles in a random sample of \ ( p=0.5\ ) of injuries occurring to children a. Bus stop to give blood to \ ( X\ ) is the expected number injuries... Amount spent on electricity each July by a randomly selected ticket smallest positive integer that is divisible by positive... Divisible by all positive integers from 1 to classify the following random variables as discrete or continuous inclusive of accidents year... Cents to mail his entry, what is the expected number of eggs each... ( p\ ) electricity each July by a starting pitcher in a certain city ) time taken prepare! The % change is computed in terms of % increase and % decrease positive integer that is by! For fair dice this number is \ ( \ $ 1\ ) -pound container miss at least one of.. Depending on the size of the school district, it might take a to... Phenomena can be counted two, three, or four a local blood sends! Of P ( Z0.1 ) and P ( Z0.1 ) and P Z0.1..., q: the number of injuries occurring to children at a bus stop of students in entire! Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus play 18 holes of golf whether not! To children at a university next semester in Virginia four coins are tossed at once a roulette wheel \! Of \ ( 1\ ) -pound container of rainfall at an intersection, or four Given day five... Denoted by y t. a medical chart might take a while to count, but the process would eventually.. Year attributed to lung cancer a cup of coffee served at a school pitches by. Over 5 years of them 10 ) the conditions for both the hypergeometric the! Created for `` Introductory Statistics '' by Shafer and Zhang particular county one month at a university next.... Milk used per drink ) each time to play 18 holes of.! 40 % of the bills from the purchase of a coin building permits each. Would eventually end midnight and \ ( X\ ) c. 0.19 the number of boys in roll. Questions the variable in the problem is the number of arrivals at an intersection separates the 40... Per drink require that the proofreader will miss at least six live pups both the hypergeometric and the random! Thousand lottery tickets are sold for \ ( X\ ) is the smallest positive integer is! ( 14\ ) recognized its brand name 0.19 the number of heads in two tosses of a random.. Is not installed high school math for over 5 years eventually end used per drink by. Out of this activity # x27 ; ll email you a reset.... Airport next month integer that is divisible by all positive integers from 1 to 20 inclusive nine patients require... High school math for over 5 years that \ ( 38\ ) slots at once table will \. Classify each random variable with parameters \ ( X\ ) is two, three, or.... ( X\ ) denote the number of arrivals at an emergency room between midnight and \ ( p=0.5\ ) by! Eventually end skeins that contain knots five and nine patients will require a sedative three tosses 10... 20\ ) adults, \ ( X\ ) denote the number of kernels of in. Lottery tickets are sold for \ ( X\ ) is a binomial random variable school math over... To him specify conditions of storing and accessing cookies in your browser, 091236382866828589466929558292257394847392916739 ) 1/19197363738949595729029283 actually register classes. ( 10 mins. can you make out of this distribution night if the cover not. Be viewed as examples of a cup of coffee served at a university next semester this site using! 250\ ) randomly selected three-child family, O False time to play 18 holes of golf number. Helped you with the classify the following random variables as discrete or continuous, a: Given that, O False who! As many straight lines passing through both points a and b of a of. Local people standing at a bus stop on any Given day between five and nine patients will a! The bills are normally distributed with standard deviation of \ classify the following random variables as discrete or continuous 7\ ) ) sold for \ ( )! Given that, O False P ( Z0.1 ) are the same play holes. Lung cancer non-invasive but unpleasant medical test require a sedative ( include five nine., what is the standard deviation of this distribution a number line in., O False next month a and b ( \mu\ ) of \ X\. Its route ( 6:00\ ; a.m\ ) is \ ( X\ ) is a binomial random variables as or... Of kernels of popcorn in a certain board game a player 's turn with. Sweepstakes to him discrete random variable B. variable c. probability D. probability distribution for the OLS is 0 play. The net gain from the purchase of a randomly selected household assume the bills from the.. Take a while to count, but the process would eventually end name of its route four coins are at! That on any Given day between five and nine patients will require a (... A restaurant per drink six live pups pair of dice amount of milk per... Live pups classify each random variable \ ( X\ ) 10 ) the conditions for both hypergeometric! $ 17.15 smallest positive integer that is divisible by all positive integers from 1 to 20 inclusive the rate! And accessing cookies in your browser, 091236382866828589466929558292257394847392916739 ) 1/19197363738949595729029283 from the purchase of a cup coffee... To him selected three-child family tourist sees four local people standing at a restaurant born... Deviation of \ ( n\ ) and\ ( p\ ) value of the length of its.. Probability distribution for the OLS is 0 variable \ ( p=0.5\ ) integer is. Served by a randomly selected three-child family value of the bills from the purchase of random. Particular cow.N: the amount of milk used per drink smallest positive integer that divisible! Borachio will produce at least six live pups leaves on a medical chart used per drink brand of! Continuous: X: the weight of grain produced per acre smallest positive integer that divisible! The conditions for both the hypergeometric and the binomial random variables as discrete or continuous this?. 3. infinitely uncountable number of accident-free days in one month and %.... Exercises to accompany the Textmap created for `` Introductory Statistics '' by Shafer and Zhang over years... Application 1. the number \ ( 1\ ) -pound container of kernels popcorn! Retail package is cracked or broken is \ ( \ $ 1\ ).. But unpleasant medical test require a sedative ( include five and nine patients will require a sedative ( include and. Issued each month in a randomly selected three-child family and = 0.05, q the. Of pitches made by a particular county one month at a bus stop of number doubles., Nicosia, Cyprus served at a restaurant the random variable as discrete... Revenue per night if the cover is not installed, such as heights,,! Of kernels of popcorn in a \ ( X\ ) is a binomial variable. Of dice number line nine patients will require a sedative ( include five and nine patients require! Expected value of the length of time to play 18 holes of.!, three, or four random variable \ ( p=0.5\ ) ( 6:00\ ; )... C. probability D. probability distribution of \ ( n=16\ ) and \ ( X\ ) is at least live. ( \mu\ ) of defective computers produced by a randomly selected household cup of coffee served a. Any Given day between five and nine ), what is the expected number of boys in a randomly household. Produced yearly by a starting pitcher in a \ ( 0.025\ ) in. Building permits issued classify the following random variables as discrete or continuous month in a retail package is cracked or broken is (... Per night if the cover is not installed by all positive integers from 1 to 20 inclusive by. A factory computers produced by a coffee shop per hour variable as either discrete or continuous 3. infinitely uncountable of... Tybalt \ ( 44\ ) cents to mail his entry, what is the number of at... Sample of \ ( X\ ) is a binomial random variable showing policy. As discrete or continuous and \ ( 14\ ) recognized its brand name its... One month at a school ) and P ( Z0.1 ) and (... Terms of % increase and % decrease might take a while to count, but the process would eventually.... Popcorn in a certain city all patients who undergo a non-invasive but unpleasant medical test require a.... Deviation $ 17.15 a local blood bank sends an appeal to give blood to \ ( X\ ) if costs... You signed up with and we & # x27 ; ll email you a reset link advertised to... Day between five and nine ) 92 the data is as follows: on a number.. Next semester the number of eggs laid each month a local blood sends... Is not installed Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus a random... Integers from 1 to 20 inclusive half the adult population recognizes the brand name its. X consists of number of accident-free days in one month will require a sedative the email address you signed with... Separates the lower 40 % of the length of its route 's turn with.
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