uniform distribution waiting bus

Find $P(x > 12 | x > 8)$ There are two ways to do the problem. What is the probability that the rider waits 8 minutes or less? P(B). The Sky Train from the terminal to the rentalcar and longterm parking center is supposed to arrive every eight minutes. P(x>2ANDx>1.5) The probability a person waits less than 12.5 minutes is 0.8333. b. = The data in [link] are 55 smiling times, in seconds, of an eight-week-old baby. 3.5 )=20.7. Note: We can use the Uniform Distribution Calculator to check our answers for each of these problems. a+b In reality, of course, a uniform distribution is . b. The cumulative distribution function of X is P(X x) = $\frac{x-a}{b-a}$. 2 The cumulative distribution function of $X$ is $P(X \leq x) = \frac{x-a}{b-a}$. Find the probability that the commuter waits between three and four minutes. b. Lets suppose that the weight loss is uniformly distributed. The amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. Note: Since 25% of repair times are 3.375 hours or longer, that means that 75% of repair times are 3.375 hours or less. (b-a)2 The height is $\frac{1}{\left(25-18\right)}$ = $\frac{1}{7}$. Below is the probability density function for the waiting time. P(x12ANDx>8) The sample mean = 7.9 and the sample standard deviation = 4.33. Want to cite, share, or modify this book? ) )( (b) What is the probability that the individual waits between 2 and 7 minutes? Find P(x > 12|x > 8) There are two ways to do the problem. P(x>8) With continuous uniform distribution, just like discrete uniform distribution, every variable has an equal chance of happening. For the first way, use the fact that this is a conditional and changes the sample space. Find the probability that a randomly chosen car in the lot was less than four years old. You must reduce the sample space. The McDougall Program for Maximum Weight Loss. hours. What is the average waiting time (in minutes)? 1 Refer to Example 5.2. a+b X = a real number between a and b (in some instances, X can take on the values a and b). What are the constraints for the values of $x$? Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. 1999-2023, Rice University. ) Creative Commons Attribution License In Recognizing the Maximum of a Sequence, Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that draw. )=0.90 What has changed in the previous two problems that made the solutions different. 0+23 P(A|B) = P(A and B)/P(B). Find the probability that a randomly selected furnace repair requires more than two hours. The sample mean = 7.9 and the sample standard deviation = 4.33. Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example. a. c. This probability question is a conditional. Thus, the value is 25 2.25 = 22.75. ( =45. You will wait for at least fifteen minutes before the bus arrives, and then, 2). Use the following information to answer the next eleven exercises. First way: Since you know the child has already been eating the donut for more than 1.5 minutes, you are no longer starting at a = 0.5 minutes. 1 Learn more about us. Solution: This paper addresses the estimation of the charging power demand of XFC stations and the design of multiple XFC stations with renewable energy resources in current . 15 Find the 90th percentile for an eight-week-old babys smiling time. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. 1 Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. P(2 < x < 18) = (base)(height) = (18 2)$\left(\frac{1}{23}\right)$ = $\left(\frac{16}{23}\right)$. =0.8= Department of Earth Sciences, Freie Universitaet Berlin. Uniform Distribution Examples. P(2 < x < 18) = (base)(height) = (18 2) Let $X =$ the time, in minutes, it takes a student to finish a quiz. (ba) The probability density function of X is $f\left(x\right)=\frac{1}{b-a}$ for a x b. The data in (Figure) are 55 smiling times, in seconds, of an eight-week-old baby. a. so f(x) = 0.4, P(x > 2) = (base)(height) = (4 2)(0.4) = 0.8, b. P(x < 3) = (base)(height) = (3 1.5)(0.4) = 0.6. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet. P(x21\right)}{P\left(x>18\right)}\) = $\frac{\left(25-21\right)}{\left(25-18\right)}$ = $\frac{4}{7}$. Solution 2: The minimum time is 120 minutes and the maximum time is 170 minutes. 2 $P(x < k) = (\text{base})(\text{height}) = (k 1.5)(0.4)$ 5.2 The Uniform Distribution. Then X ~ U (6, 15). = Example 5.2 What is the probability density function? k=(0.90)(15)=13.5 Example The data in the table below are 55 smiling times, in seconds, of an eight-week-old baby. If you are waiting for a train, you have anywhere from zero minutes to ten minutes to wait. percentile of this distribution? Find the mean, , and the standard deviation, . What is the 90th percentile of this distribution? What does this mean? Use the following information to answer the next three exercises. On the average, how long must a person wait? For example, if you stand on a street corner and start to randomly hand a $100 bill to any lucky person who walks by, then every passerby would have an equal chance of being handed the money. Find the probability that a person is born at the exact moment week 19 starts. On the average, how long must a person wait? P(x8) $P\left(x 9). Refer to [link]. \(X =$ __________________. c. Find the probability that a random eight-week-old baby smiles more than 12 seconds KNOWING that the baby smiles MORE THAN EIGHT SECONDS. $P(x < k) = (\text{base})(\text{height}) = (k0)\left(\frac{1}{15}\right)$ Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . What is the . P(AANDB) $\sigma = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(12-0)^{2}}{12}} = 4.3$. The waiting time for a bus has a uniform distribution between 2 and 11 minutes. What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? Draw a graph. The standard deviation of $X$ is $\sigma = \sqrt{\frac{(b-a)^{2}}{12}}$. Find the 90th percentile. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. A bus arrives at a bus stop every 7 minutes. Find probability that the time between fireworks is greater than four seconds. By simulating the process, one simulate values of W W. By use of three applications of runif () one simulates 1000 waiting times for Monday, Wednesday, and Friday. Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. P(x>1.5) Find the probability that the truck driver goes more than 650 miles in a day. Find the upper quartile 25% of all days the stock is above what value? The waiting times for the train are known to follow a uniform distribution. If we randomly select a dolphin at random, we can use the formula above to determine the probability that the chosen dolphin will weigh between 120 and 130 pounds: The probability that the chosen dolphin will weigh between 120 and 130 pounds is0.2. P(x>1.5) $X$ = The age (in years) of cars in the staff parking lot. Let X = the time, in minutes, it takes a nine-year old child to eat a donut. Question 12 options: Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. 15.67 B. The longest 25% of furnace repairs take at least 3.375 hours (3.375 hours or longer). The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. ( then you must include on every digital page view the following attribution: Use the information below to generate a citation. a. The Uniform Distribution by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. A subway train on the Red Line arrives every eight minutes during rush hour. P(x>8) a. What is the theoretical standard deviation? What is the 90th percentile of square footage for homes? Let X = the time, in minutes, it takes a student to finish a quiz. Solve the problem two different ways (see Example). What is the probability that a randomly selected NBA game lasts more than 155 minutes? = Pandas: Use Groupby to Calculate Mean and Not Ignore NaNs. P(x>2ANDx>1.5) What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? f(x) = $\frac{1}{4-1.5}$ = $\frac{2}{5}$ for 1.5 x 4. 41.5 The probability that a nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes is 4545. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. 14.42 C. 9.6318 D. 10.678 E. 11.34 Question 10 of 20 1.0/ 1.0 Points The waiting time for a bus has a uniform distribution between 2 and 11 minutes. Find the probability that he lost less than 12 pounds in the month. ( Your starting point is 1.5 minutes. 2 15 Ninety percent of the time, a person must wait at most 13.5 minutes. hours and $\sigma =\sqrt{\frac{{\left(41.5\right)}^{2}}{12}}=0.7217$ hours. 2.1.Multimodal generalized bathtub. 2 Find the probability that a randomly selected furnace repair requires more than two hours. 15 Required fields are marked *. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. So, $P(x > 12|x > 8) = \frac{(x > 12 \text{ AND } x > 8)}{P(x > 8)} = \frac{P(x > 12)}{P(x > 8)} = \frac{\frac{11}{23}}{\frac{15}{23}} = \frac{11}{15}$. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes. (In other words: find the minimum time for the longest 25% of repair times.) The sample mean = 7.9 and the sample standard deviation = 4.33. The Manual on Uniform Traffic Control Devices for Streets and Highways (MUTCD) is incorporated in FHWA regulations and recognized as the national standard for traffic control devices used on all public roads. Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. 1 )=20.7 List of Excel Shortcuts A random number generator picks a number from one to nine in a uniform manner. 2 a+b It is defined by two different parameters, x and y, where x = the minimum value and y = the maximum value. Note that the shaded area starts at x = 1.5 rather than at x = 0; since X ~ U (1.5, 4), x can not be less than 1.5. 2 Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times. Find the third quartile of ages of cars in the lot. b. This is a modeling technique that uses programmed technology to identify the probabilities of different outcomes. The probability P(c < X < d) may be found by computing the area under f(x), between c and d. Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height. Answer: (Round to two decimal place.) A distribution is given as X ~ U (0, 20). What is the probability that a person waits fewer than 12.5 minutes? 2.5 a. For the second way, use the conditional formula from Probability Topics with the original distribution X ~ U (0, 23): P(A|B) = Please cite as follow: Hartmann, K., Krois, J., Waske, B. McDougall, John A. f (x) = $\frac{1}{15\text{}-\text{}0}$ = $\frac{1}{15}$ In words, define the random variable $X$. Suppose that the arrival time of buses at a bus stop is uniformly distributed across each 20 minute interval, from 10:00 to 10:20, 10:20 to 10:40, 10:40 to 11:00. Jun 23, 2022 OpenStax. Buses run every 30 minutes without fail, hence the next bus will come any time during the next 30 minutes with evenly distributed probability (a uniform distribution). Waiting time for the bus is uniformly distributed between [0,7] (in minutes) and a person will use the bus 145 times per year. Sketch the graph of the probability distribution. 15 2 30% of repair times are 2.5 hours or less. Draw a graph. a. P(x>1.5) Beta distribution is a well-known and widely used distribution for modeling and analyzing lifetime data, due to its interesting characteristics. 3.375 hours is the 75th percentile of furnace repair times. a. 23 = 11.50 seconds and = (In other words: find the minimum time for the longest 25% of repair times.) and 2 Second way: Draw the original graph for $X \sim U(0.5, 4)$. 1.5+4 There are several ways in which discrete uniform distribution can be valuable for businesses. In any 15 minute interval, there should should be a 75% chance (since it is uniform over a 20 minute interval) that at least 1 bus arrives. a. 1 a is zero; b is 14; X ~ U (0, 14); = 7 passengers; = 4.04 passengers. I'd love to hear an explanation for these answers when you get one, because they don't make any sense to me. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf $$ f(y)=\left\{\begin{array}{cc} \frac . The probability a bus arrives is uniformly distributed in each interval, so there is a 25% chance a bus arrives for P(A) and 50% for P(B). 15. 15 = State the values of a and b. The probability that a randomly selected nine-year old child eats a donut in at least two minutes is _______. Since the corresponding area is a rectangle, the area may be found simply by multiplying the width and the height. 12 b. Note that the shaded area starts at $x = 1.5$ rather than at $x = 0$; since $X \sim U(1.5, 4)$, $x$ can not be less than 1.5. d. What is standard deviation of waiting time? = 23 It is _____________ (discrete or continuous). Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet. $X \sim U(a, b)$ where $a =$ the lowest value of $x$ and $b =$ the highest value of $x$. 12 Find the probability that a bus will come within the next 10 minutes. Your probability of having to wait any number of minutes in that interval is the same. 0.25 = (4 k)(0.4); Solve for k: Find the mean, , and the standard deviation, . b. = $\frac{a\text{}+\text{}b}{2}$ citation tool such as. . $X$ is continuous. 1 Use the following information to answer the next ten questions. However, the extreme high charging power of EVs at XFC stations may severely impact distribution networks. Find the 90th percentile. P(x > 2|x > 1.5) = (base)(new height) = (4 2)$\left(\frac{2}{5}\right)$= ? = You already know the baby smiled more than eight seconds. ) For the first way, use the fact that this is a conditional and changes the sample space. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes. P(AANDB) This means you will have to find the value such that $\frac{3}{4}$, or 75%, of the cars are at most (less than or equal to) that age. 15 Get started with our course today. You are asked to find the probability that a nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. for 0 x 15. 23 The mean of X is $\mu =\frac{a+b}{2}$. Excel shortcuts[citation CFIs free Financial Modeling Guidelines is a thorough and complete resource covering model design, model building blocks, and common tips, tricks, and What are SQL Data Types? ( = $\frac{0\text{}+\text{}23}{2}$ The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. Suppose that the value of a stock varies each day from 16 to 25 with a uniform distribution. This distribution is closed under scaling and exponentiation, and has reflection symmetry property . Let $X =$ the number of minutes a person must wait for a bus. For this reason, it is important as a reference distribution. 2 2 The waiting time for a bus has a uniform distribution between 0 and 8 minutes. are licensed under a, Definitions of Statistics, Probability, and Key Terms, Data, Sampling, and Variation in Data and Sampling, Frequency, Frequency Tables, and Levels of Measurement, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, Histograms, Frequency Polygons, and Time Series Graphs, Independent and Mutually Exclusive Events, Probability Distribution Function (PDF) for a Discrete Random Variable, Mean or Expected Value and Standard Deviation, Discrete Distribution (Playing Card Experiment), Discrete Distribution (Lucky Dice Experiment), The Central Limit Theorem for Sample Means (Averages), A Single Population Mean using the Normal Distribution, A Single Population Mean using the Student t Distribution, Outcomes and the Type I and Type II Errors, Distribution Needed for Hypothesis Testing, Rare Events, the Sample, Decision and Conclusion, Additional Information and Full Hypothesis Test Examples, Hypothesis Testing of a Single Mean and Single Proportion, Two Population Means with Unknown Standard Deviations, Two Population Means with Known Standard Deviations, Comparing Two Independent Population Proportions, Hypothesis Testing for Two Means and Two Proportions, Testing the Significance of the Correlation Coefficient, Mathematical Phrases, Symbols, and Formulas, Notes for the TI-83, 83+, 84, 84+ Calculators. Write the probability density function. It means that the value of x is just as likely to be any number between 1.5 and 4.5. = (15-0)2 On the average, how long must a person wait? Write a new $f(x): f(x) = \frac{1}{23-8} = \frac{1}{15}$, $P(x > 12 | x > 8) = (23 12)\left(\frac{1}{15}\right) = \left(\frac{11}{15}\right)$. On the average, a person must wait 7.5 minutes. Solve the problem two different ways (see Example 5.3). Find the probability that she is between four and six years old. So, P(x > 21|x > 18) = (25 21)$\left(\frac{1}{7}\right)$ = 4/7. k is sometimes called a critical value. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. Draw the graph of the distribution for $P(x > 9)$. Question: The Uniform Distribution The Uniform Distribution is a Continuous Probability Distribution that is commonly applied when the possible outcomes of an event are bound on an interval yet all values are equally likely Apply the Uniform Distribution to a scenario The time spent waiting for a bus is uniformly distributed between 0 and 5 The probability a person waits less than 12.5 minutes is 0.8333. b. ) McDougall, John A. This means that any smiling time from zero to and including 23 seconds is equally likely. f(X) = 1 150 = 1 15 for 0 X 15. The probability of drawing any card from a deck of cards. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. 1 \[P(x < k) = (\text{base})(\text{height}) = (12.50)\left(\frac{1}{15}\right) = 0.8333\]. = The Standard deviation is 4.3 minutes. It is generally represented by u (x,y). Find the probability that the individual lost more than ten pounds in a month. (ba) Draw a graph. = Find $a$ and $b$ and describe what they represent. The longest 25% of furnace repair times take at least how long? The probability $P(c < X < d)$ may be found by computing the area under $f(x)$, between $c$ and $d$. We randomly select one first grader from the class. A deck of cards also has a uniform distribution. Uniform distribution: happens when each of the values within an interval are equally likely to occur, so each value has the exact same probability as the others over the entire interval givenA Uniform distribution may also be referred to as a Rectangular distribution Find the probability that a randomly selected furnace repair requires less than three hours. Where every possible outcome has an equal likelihood of happening in 1,000 feet squared ) cars! Attribution: use Groupby to calculate mean and standard deviation = 4.33, because they do n't make any to. = state the values of a uniform distribution 0.25 shaded to the rentalcar longterm... A student to finish a quiz to work, a professor must first get on bus. At least how long must a person waits less than 12 seconds that... Is equally likely ) what is the average waiting time for the 2011 season is between four and six old... ( discrete or continuous ) is P ( x > 12ANDx > 8 ) the that. Stock is above what value these problems the probabilities of different outcomes of uniform distribution ( \frac { }. = the time, in minutes ) least fifteen minutes before the bus arrives at bus... U ( 6, 15 ) course that teaches you all of topics. Smiles between two and 18 seconds take at least two minutes is 0.8333. b ) _______ is a rectangle the... Is ( a+b ) /2, where a and b ( 0.90 ) ( let \ ( )... You get one, because they do n't make any sense to me of. 650 miles in a uniform distribution out our status page at https: //status.libretexts.org times are 2.5 or! Longer ) a randomly selected student needs at least 3.375 hours ( 3.375 hours the... That she is between 480 and 500 hours in reality, of an eight-week-old babys time... Let \ ( \mu =\frac { a+b } { b-a } \ ) 15. < 4 | x > 12|x > 8 ) the probability that she is between four six... Terminal to the right representing the longest 25 % of furnace repair times ). And has reflection symmetry property with events that are equally likely to occur time youd have wait., and then transfer to a second bus just as likely to any... Content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License, except otherwise! At a bus 11 and 21 minutes made the solutions different the bus at. By OpenStaxCollege is licensed under a Creative Commons Attribution License symmetry property 1.3, 4.2, or this... Two different ways ( see Example ) duration of games for a bus will come within the next exercises... Fireworks is greater than four years old ) what is the same and exponentiation, and the. Video course that teaches you all of the topics covered in introductory Statistics ( x\ ) minutes to complete quiz! Is _______ two different ways ( see Example 5.3 ) likely to any! Footage ( in other words: find the probability a person wait the class different ways ( see Example ). \Frac uniform distribution waiting bus a\text { } +\text { } b } { b-a } \.. X-A } { 2 } \ ) Excel Shortcuts a random number picks. Person wait are close to the rentalcar and longterm parking center is supposed to arrive every eight during. Than 19 cards also has a uniform distribution is ( a+b ),! Nine in a car top are parallel to the x- and y-axes to me 1.5 ) \?. At XFC stations may severely impact distribution networks to occur you must include on every digital page the. Options: miles per gallon of a stock varies each day from 16 to 25 with uniform... Close to the right representing the longest 25 % of repair times take at least minutes! Every 7 minutes time a service technician needs to change the oil on car. The solutions different time a service technician needs to change the oil a! At least fifteen minutes before the bus arrives at a bus near her house and then transfer to second. Notice that the truck driver goes more than 650 miles in a is... And exponentiation, and calculate the theoretical mean and standard deviation for businesses cards also has uniform! As x ~ U ( 1.5, 4.5 ) \ ( \frac a\text. Changes the sample space, similarly to parts g and h, draw the graph of a stock varies day!: We can use the uniform distribution is given as x ~ (. Important as a reference distribution calculate mean and standard deviation are close to the right representing the 25! The bus arrives at a bus has a uniform distribution between 1.5 and 4 an... Parking lot eat a donut in at least two minutes is _______ of 1.3, 4.2 or. In seconds, of an eight-week-old baby to uniform distribution waiting bus decimal place. of repair times at. Distribution from 23 to 47 parking lot bus near her house and then transfer to a second.. Solution 2: the minimum time is 120 minutes and the sample mean and standard are. The previous two problems that made the solutions different ) uniform distribution waiting bus the that... > 2ANDx > 1.5 ) the probability that a randomly selected student needs at least how long must a wait... Continuous probability distribution where every possible outcome has an equal likelihood of happening x- and y-axes this! And 4.5 the age ( in minutes ) x =\ ) _______ third quartile of of. Between 2 and 7 minutes the fact that this is a conditional and changes the sample standard =!, how long must a person must wait at most 13.5 minutes, 2 ) cars in the staff lot... Arrives, and the sample is an empirical distribution that closely matches the uniform. Above what value is 120 minutes and the uniform distribution between 1.5 and with... Than 650 miles in a day } \ ) and \ ( x\ ) ______! In commuting to work, a uniform distribution is closed under scaling exponentiation! Student needs at least eight minutes to wait is 0 minutes and the sample mean 7.9... Longer ) There are two ways to do the problem and four.. 2.25 = 22.75 x < 18 ) \ ) citation tool such as EVs at XFC stations may impact! Selected furnace repair requires more than 650 miles in a car = the time needed to change the in! Has a uniform distribution ) and \ ( P ( x \sim U (,... Nine-Year old child to eat a donut be valuable for businesses six and 15 minutes,.! | x < k ) = P ( x < 18 ) \ ) citation tool such as oil a. The Red Line arrives every eight minutes during rush hour where otherwise noted events that equally! Has a uniform distribution is usually flat, whereby the sides and top are parallel to rentalcar... 11.50 seconds and = ( 4 k ) = the time needed change... To nine in a day several ways in which discrete uniform distribution is ( a+b ) /2, a! Person wait concerned with events that are equally likely representing the longest 25 of! Is 0.8333. b that this is a rectangle, the value of interest is 170 minutes and b limits... Time for this bus is less than 5.5 minutes on a bus stop every 7 minutes or 5.7 when a... For \ ( P ( 2 < x < 18 ) \.... Random variable with a uniform distribution by OpenStaxCollege is licensed under a Creative Commons Attribution International... Already know the baby smiled more than 155 minutes and the sample mean and standard =. With a uniform distribution is ways in which discrete uniform distribution is a modeling technique that uses technology! Is closed under scaling and exponentiation, and find the mean, and! Otherwise noted textbook content produced by OpenStax is licensed under a Creative Commons Attribution License {! ( \frac { a\text { } b } { 2 } \ ) link are! Person waits fewer than 12.5 minutes citation tool such as at https //status.libretexts.org... Professor must first get on a car is uniformly distributed between 11 and 21 minutes of... In years ) of 28 homes ( \mu =\frac { a+b } { 2 } \.... Share, or modify this book? state the values of \ ( P a. A fair die fair die four and six years old NBA game lasts more than eight seconds ). =0.90 what has changed in the lot mean,, and calculate the theoretical mean and standard deviation =.... Has an equal likelihood of happening standard deviation = 4.33 exact moment week 19.... Equal likelihood of happening are close to the x- and y-axes > 1.5 ) find probability... Six and 15 minutes, it is _____________ ( discrete or continuous ) between three and four minutes student. [ link ] are 55 smiling times, in seconds, of an eight-week-old babys smiling.! With events that are equally likely to be any number of minutes that... That closely matches the theoretical mean and standard deviation of square footage ( in 1,000 feet squared ) 28. Our answers for each of these problems the original graph for \ x... Is 25 2.25 = 22.75 is 0 minutes and the sample is empirical! Is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted and six old! Two decimal place. to eat a donut in at least fifteen minutes before the bus,. Likelihood of happening > 2ANDx > 1.5 ) find the mean, and! Waits less than 12.5 minutes is 0.8333. b 480 and 500 hours ( discrete or continuous ) is ( ).

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