Probability Questions and Answers

A recent survey found that 40 of IRSC students plan to go on a vacation after graduation Suppose 5 IRSC students are randomly selected and let x be the number of students that plan to go on a vacation after graduation out of the sample of 5 Use the binomial probability formula or the binomial probability table to construct the probability distribution of x Also use the binomial probability formula or the binomial probability table to construct the cumulative probability distribution of Round solutions to four decimal places if necessary xP x 2 3 4 5 xP X x 0 1 2 3 4 5 Calculate the probability that no more than 2 students out of a random sample of 5 students plan to go on vacation after graduation P x 2 Calculate the probability that more than 2 students out of a random sample of 5 students plan to go on vacation after graduation P x 2

The Florida lottery has a game called Pick 4 where a player pays 1 and then picks a sequence of four numbers 0 9 e g 1234 0389 9020 If the four numbers come up in the order you picked then you win 3800 a Write the probability distribution for a player s winnings Fill in the table below Enter the left column values from smallest to largest Round solutions to four decimal places if necessary P x I b What are your expected winnings Round the solution to two decimal places since this value is interpreted as dollars E x c Which of the following is the correct interpretation of the expected winnings Select an answer

The following table gives the probability distribution of a discrete random variable X Use the table to find the following probabilities Round solutions to three decimal places if necessary xP x 0 0 039 1 0 088 2 0 147 3 0 158 4 0 176 5 0 196 6 0 196 P x 5 P x 1 P x 3 P 1 x 4 The shape of the probability distribution is Solest

Delta Airlines flights from Orlando to New York are on time 60 of the time Suppose 7 flights are randomly selected and the number on time flights is recorded Determine the following probabilities Round solutions to four decimal places if necessary The probability that exactly 6 flights are on time is P x 6 The probability that at most 4 flights are on time is P x 4 The probability that at least 4 flights are on time is P x 4

Andrew finds that on his way to work his wait time for the bus is roughly uniformly distributed between 15 minutes and 23 minutes One day he times his wait and writes down the number of minutes ignoring the seconds Round solutions to three decimal places if necessary 0 12 0 1 0 08 0 06 0 04 0 02 15 16 17 18 19 20 21 Wait time measured in minutes rounded down 22 What is the probability that Andrew waits for 18 minutes P X 18 What is the probability that Andrew waits between 15 and 18 minutes P 15 X 18

16 7 Points DETAILS The postage charged for first class mail is a function of its weight A postal service uses the fol Rate 0 44 0 23 HARMATHAP12 2 4 051 Weight Increment First ounce or fraction of an ounce Each additional ounce or fraction a Convert this table to a piecewise defined function that represents postage for letter P x b Find P 1 8 0 x 1 1 x 2 if 2 x 3 if 3 x 4 if if

why not 15 Car Fatalities The recent rate of car fatalities was 33 561 fatalities for 2969 billion miles traveled based on data from the National Highway Traffic Safety Administration Find the probability that for the next billion miles traveled there will be at least one fatality What does the result indicate about the likelihood of at least one fatality 191 checks Find the probability that on a

In Exercises 9 16 use the Poisson distribution to find the indicated probabilities ber of births per day then use that result to find the probability that in a day there are 15 births Does it appear likely that on any given day there will be exactly 15 births 9 Births In a recent year NYU Langone Medical Center had 4221 births Find the mean num ders In a recent year there were 333 murde

the result indicate about the 16 Checks In a recent year the author wrote 181 checks Find the probability that on randomly selected day he wrote at least one check

A real estate agent conducted an experiment to test the effect of selling a staged home vs selling an empty home To do so the agent obtained a list of 10 comparable homes just listed for sale that were currently empty He randomly assigned 5 of the homes to be staged meaning filled with nice furniture and decorated The owners of the 5 homes all agreed to have their homes staged by professional decorators The other 5 homes remained empty The hypothesis is that empty homes are not as appealing to buyers as staged homes and therefore sell for lower prices than staged homes The mean selling price of the 5 empty homes was 150 000 with a standard deviation of 22 000 The mean selling price of the 5 staged homes was 175 000 with a standard deviation of 35 000 A dotplot of each sample shows no strong skewness and no outliers The agent tests Ho H H 0 H H H 0 where P the true mean selling price of all comparable empty homes and the true mean selling price of all comparable staged homes The conditions for inference are met What are the values of the test statistic and P value for a f test about a difference in means Find the t table here O 150 000 175 000 22 000 35 000 5 0 10 and 0 15 O 150 000 175 000 22 000 35 000 10 30 The P value is between The P value is between

day there will be exactly 15 births 10 Murders In a recent year there were 333 murders in New York City Find the mean num murders Does it appear that there are expected to be many days with no murders ber of murders per day then use that result to find the probability that in a day there are no active Decay Radioactive atoms are unstob be Does it appear much energV

11 Radioactive Decay Radioactive atoms are unstable because they have too much energy When they release their extra energy they are said to decay When studying cesium 137 a nuclear engineer found that over 365 days 1 000 000 radioactive atoms decayed to 977 287 radioactive atoms therefore 22 713 atoms decayed during 365 days 2 Find the mean number of radioactive atoms that decayed in a day Find the probability that on a given day exactly 50 radioactive atoms decayed murde

had exactly 2 hits 14 Disease Cluster Neuroblastoma a rare form of cancer occurs in 11 children in a million so its probability is 0 000011 Four cases of neuroblastoma occurred in Oak Park Illinois which had 12 429 children a Assuming that neuroblastoma occurs as usual find the mean number of cases in groups of 12 429 children b Using the unrounded mean from part a find the probability that the number of neuroblas toma cases in a group of 12 429 children is 0 or 1 c What is the probability of more than one case of neuroblastoma d Does the cluster of four cases appear to be attributable to random chance Why or why not for 2969 billion mile

The table shows the educational attainment of the population of a country ages 25 and over expressed in millions Find the probability that a randomly selecte person age 25 or over has completed four years of high school only or somo college but less than four years 0 Tyne an integer or a simplifind fraction The probability is Male Female Total Years of High School Less than 4 16 14 30 4 only 27 25 52 Years of College Some less than 4 18 25 43 CICLOS 4 or more i 18 19 37 Total 79 83 162

Solve the following questions 6 9 Question 6 0 5 View O 0 0625 O 0 028 ke and Screen Shot 2023 0 Q Q Zoom Find the probability that exactly half of the fish that are caught will be Trout are as easy to catch as the Bass a Share Highlight Rotate Markup Search 1 pts

1 6 pts Based on past results found in the Information Please Almanac there is a 0 1919 probability that a baseball World Series will last four games a 0 2121 probability that it will last five games a 0 2223 probability that it will last six games and a 0 3737 probability that it will last seven games a Does the given information describe a probability distribution Explain b Assuming that the given information describes a probability distribution find the mean and standard deviation for the number of games in World Series including units

p x Solve the following questions 1 5 D A Question 3 Find the variance of X O 1 67 02 0 3 O 11 2 0 2 1 0 2 Aa 2 0 3 4 0

3 6 pts Tree diameters in a plot of land are normally distributed with a mean of 14 inches and a standard deviation of 3 2 inches Define draw a label a Normal curve and find the answers using Onlinestatbook You only need to fully label the first drawing a What is the probability that an individual tree has a diameter between 13 inches and 16 3 inches b What is the probability that an individual tree has a diameter less than 12 inches c What is the probability that an individual tree has a diameter of at least 15 inches

that there are lots of them in the lake and that the Trout are as easy to catch as the Bass Solve the following questions 6 9 Question 7 0 684 Find the probability that one or more Trout will be caught O 0 75 View 0422 0 9316 Screen Shot 2023 02 1 Q Q B Zoom Share Highlight Rotate Markup 1 p

Suppose X is a discrete random variable with the probability distribution function X p x Solve the following questions 1 5 Question 1 Find P X 0 0 3 0 0 2 2 0 3 0 5 1 0 2 1 0 2 2 0 3

A survey of 300 randomly selected high school students determined that 239 play organized sports a What is the probability that a randomly selected high school student plays organized sports b Interpret this probability a The probability that a randomly selected high school student plays organized sports is Round to the nearest thousandth as needed

If a person rolls a six sided die and then draws a playing card and checks its color describe the sample space possible outcomes using 1 2 3 4 5 6 for the die outcomes and B R for the card outcomes The sample space is S Use a comma to separate answers as needed

Which of the following numbers could be the probability of an event 1 0 51 1 5 0 08 0 28 0 The numbers that could be a probability of an event are Use a comma to separate answers as needed

Based on historical data your manager believes that 27 of the company s orders come from first time customers A random sample of 119 orders will be used to estimate the proportion of first time customers What is the probability that the sample proportion is less than 0 31 Answer Enter your answer as a number accurate to 4 decimal places Question Help Post to forum

According to a 2009 Reader s Digest article people throw away approximately 11 of what they buy at the grocery store Assume this is the true proportion and you plan to randomly survey 105 grocery shoppers to investigate their behavior What is the probability that the sample proportion exceeds 0 15 Answer Enter your answer as a number accurate to 4 decimal places Question Help Post to forum

A Food Marketing Institute found that 32 of households spend more than 125 a week on groceries Assume the population proportion is 0 32 and a simple random sample of 211 households is selected from the population What is the probability that the sample proportion of households spending more than 125 a week is less than 0 34 Answer Enter your answer as a number accurate to 4 decimal places Question Help Post to forum

Based on historical data your manager believes that 29 of the company s orders come from first time customers A random sample of 124 orders will be used to estimate the proportion of first time customers What is the probability that the sample proportion is greater than 0 26 Answer Question Help Enter your answer as a number accurate to 4 decimal places Bort to foru

Here are the scores of 14 students on a history 58 60 61 65 69 69 75 75 78 Notice that the scores are ordered from least to Give the five number summary and the interqu Five number summary Minimum Lower quartile 0 Median 0 Upper quartile Maximum 0

Suppose you are the director of human resources for a company You recently posted a job opening and have received so many applications that you decide to call in randomly chosen applications for interviews You select 8 resumes at random from all that were submitted in response to the job posting Suppose you know that overall 40 of resumes are from applicants who have 10 or more years experience What is the probability that at least 2 of the resumes chosen will list at least 10 years experience

On each trial of an experiment a subject is p

The annual amounts of rainfall in a certain region are modeled usi The mean of the distribution is 30 8 cm and the standard deviation n the figure V is a number along the axis and is under the highe nd U and Ware numbers along the axis that are each the same se the empirical rule to choose the best value for the percentage Percentage of total area shaded

The red blood cell counts 52 49 55 50 49 Send data to calcul

Thorny cover None 1 3 1 3 to 2 3 B 2 3 Yes 60 76 44 29 No 151 158 177 176 Our experiment is to pick one tree at random form the entire sample i Make the marginal counts for Thorny Cover and for Deer Damage ii What is the probability of selecting a tree that is damaged AND had no thorny cover iii What is the probability of selecting a tree that is damaged iv What is the probability of selecting a tree that had no thorny cover v What is the probability of selecting a tree that is either damaged OR had no thorny cover b Our experiment is again to pick one tree at random form the entire sample i What is the probability of selecting a tree that had no cover AND had 2 3 cover Hint Can a tree be in BOTH of these conditions ii What is the probability that a randomly selected tree has either no cover OR 2 3 cover c Convert the entire table of counts and marginals to percents These will all be percents of the total sample size These are called the joint inside probability distribution and the two marginal distributions

6 Stacked StatTutor Continuous probability models

17 Find the probability that the number x of correc 1902Y 18 Find the probability that the number x of correct answers is no more than 2 d the probability of no correct answers

sify the outcomes described in each scenario as m Mutually exclusive

obabilities can be determined mathematically empiric oretical classical and a priori Which of the followin An environmentalist believes that there is a 15 cha years When presented with 10 pictures of different birds birds so the estimated probability that the program picture is 70 The Rocky Mountains mainly cover six different sta

prizes at a carnival tossing game are different stuffed animals There are 34 tigers 27 bears 12 hippopotamuses lo affes and 22 monkeys The carnival manager randomly selects a prize when a player wins the game etermine the probability that the prize selected is not a hippopotamus Give your answer as a decimal precise to three ecimal places I Probability

8 2 Probability is a measure of how likely an event is to occur Ma given The probability value is usually a more exact measure a This event is impossible It can never occur b This event is certain It will ocur on every trial e This event is very unlikely but it will occur once in a whi

Q2 The random variable X is the amount of money that a randomly selected adult has in his her possession X is rounded to the nearest ten dollars 10 0 20 20 0 15 30 0 25 40 0 20 X 0 P X 0 10 A What is the mean or expected value of X Interpret this value in context B What is the standard deviation of X Interpret this value in context 50 0 10

Consider the following data Step 3 of 3 Determine if the data set is unimod Answer Separate multiple modes with commas if necess

The z score corresponding to the beginning of the shaded region is 0 5 Using your standard normal distribution table calculate the total area of the shaded region 2 0 2

Make a scatter diagram for the data Use the scatter diagram to describe how if at all the variables are related Subject ABCDEFGO Time watching TV x 14 10 8 13 13 11 12 Time on Internet y 10 8 4 13 14 5 14 OA The variables appear to be negatively linearly related 20 B The variables do not appear to be linearly related 20 Q The variables appear to be positively linearly related Q 20 Do The variables do nd appear to be linearly related Q

Scores for a common standardized college aptitude test are normally distributed with a mean of 516 and a standard deviation of 96 Randomly selected students are given a Test Prepartion Course before taking this test Assume for sake of argument that the course has no effect If 1 of the students is randomly selected find the probability that their score is at least 543 9 P X 543 9 Enter your answer as a number accurate to 4 decimal places If 17 of the students are randomly selected find the probability that their mean score is at least 543 9 P X 543 9 Enter your answer as a number accurate to 4 decimal places

A population of values has a normal distribution with random sample of size n 226 52 1 and o 79 6 You intend to draw a Find the probability that a single randomly selected value is between 46 8 and 47 9 P 46 8 X 47 9 Find the probability that a sample of size n 226 is randomly selected with a mean between 46 8 and 47 9 P 46 8 X 47 9 Enter your answers as numbers accurate to 4 decimal places

The manager of a computer retail store is concerned that their suppliers have been giving them laptop computers with lower than average quality Their research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 2 years and a standard deviation of 0 5 years They randomly select records on 49 laptops sold in the past and find that the mean replacement time is 4 years Assuming that the laptop replacement times have a mean of 4 2 years and a standard deviation of 0 5 years find the probability that 49 randomly selected laptops will have a mean replacement time of 4 years or less P X 4 years Enter your answer imber decimal places

Each year about 1500 students take the introductory statistics course at a large university This year scores on the final exam are distributed with a median of 74 points a mean of 70 points and a standard deviation of 10 points There are no students who scored above 100 the maximum score attainable on the final but a few students scored below 20 points a Is the distribution of scores on this final exam symmetric right skewed or left skewed left skewed Oright skewed O symmetric Or b Would you expect most students to have scored above or below 70 points above O below c What is the probability that the average score for a random sample of 40 students is above 75 x please round to four decimal places

Use the linear correlation coefficient given to determine the coefficient of determination R2 rounding to two decim places r 0 88 OA R 7 744 OB R 9 38 OC R 77 44 OD R 93 81 HEE

Using the standard Normal distribution tables the area under the standard Normal curve corresponding to 0 5 Z 1 2 is 0 2815 0 3085 0 8849

A poll was conducted of more than 50 000 buyers of new cars 90 days after the cars were purchased The data on problems per 100 vehicles for cars made by Toyota and General Motors GM are given in the time plot below for the years 1998 2004 The solid line is for GM and the dashed line is for Toyota Problems per 100 whicles 190 180 170 160 150 140 130 Tim Deries Plot of Problems per 100 Vehicles for GM and Tet 120 110 000 100 1990 1000 Year 2002 In 2002 the number of problems per 100 vehicles was about 20 higher for GM than for Toyota about twice as high for Toyota than for GM about twice as high for GM as for Toyota 2004 VIO OM Trys