Probability Questions and Answers

In a questionnaire a random sample of teachers were asked whether they provide extra credit to students in their class The questionnaire resulted in a sample proportion of p 0 27 with a sampling standard deviation of op 0 03 who mentioned they provide extra credit Using the empirical rule write a 99 7 confidence interval for the true proportion of teachers who provide extra credit Provide your answer below

A researcher is trying to estimate the population mean for a certain set of data The sample mean is 45 and the error bound for the mean is 9 at a 99 7 confidence level So 45 and EBM 9 Find and interpret the confidence interval estimate Select the correct answer below O We can estimate with 99 7 confidence that the true value of the population mean is between 42 and 48 O We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 54 O We can estimate with 99 7 confidence that the true value of the population mean is between 45 and 54 We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 54 O We can estimate with 99 7 confidence that the true value of the population mean is between 39 and 51 We can estimate with 99 7 confidence that the true value of the population mean is between 36 and 45

The probability density function of a continuous random variable X is given by 0 x 1 1 2 elsewhere T fx x 2 z 0 a What is the probablilty that X is between 1 and 2 b Find the expected value of X c Find the standard deviation of X 2 marks e Sketch or plot the PDF in the range 1 a 3 this must include all relevant features and labels 1 mark 1 mark 2 marks

A certain type of mango that weighs over 425 grams is considered to be large in size The weights for this type of mango X grams are normally distributed with a mean of 400 and a standard deviation of 25 Find the probability that a randomly selected mango of this type will not be considered as large size Round your answer to four decimal places Provide your answer below

A random sample of adult reaction times has a sample mean of 394 3 milliseconds and a sample standard deviation of s 84 6 milliseconds Use the Empirical Rule to determine the approximate percentage of adult reaction times that lie between 140 5 and 648 1 milliseconds Round your answer to the nearest tenth Provide your answer below

Hugo averages 22 points per basketball game with a standard deviation of 4 points Suppose Hugo s points per basketball game are normally distributed Let X the number of points per basketball game Then X N 22 4 Provide your answer below Suppose Hugo scores 7 points in the game on Sunday The z score when x 7 is This z score tells you that x 7 is standard deviations to the left of the mean The mean is

I can calculate the profit or loss from a stock sale 6 lifelong How I Did Circle one I m still learning it Elean Schenandore purchased 300 shares of CY Energy stock online and paid a total of 8 484 95 She sold the stock at 39 94 per share and paid a 39 95 sales commission a What was the net amount of the sale b What was the profit or loss from th e 1 point Personal Finance B I got it

Let us play a game of tossing coins A total of three fair coins are tossed each time You receive one point for each head and two points for each tail For example you would receive four 4 points if a toss yields two heads and one tail Define the number of points you receive in each toss as X a Analytical analysis Determine the probability distribution function of X i e fx x and show the analytical results using either a bar chart or histogram b Experiments Toss the three coins 30 times and create a table to record the outcomes i e number of points and their associated number of occurrence Plot the experimental results using either a bar chart or histogram Horizontal axis value of x or outcome value vertical axis relative frequency of the occurrence or number of occurrence 30 c Discussions Compare the results in a and b and discuss

The values and relative frequencies for a set of data are shown below Complete the cumulative relative frequency table Provide your answer below Data Value Relative Frequency Cumulative Relative Frequency 1 2 3 0 21 0 18 0 34 027

Suppose that f is a continuous function We observe f a f b 0 in the range of a b Which of the following is correct There is only one root There is an undeterminable number of roots There is no root There is at least one root

What is the formula used to calculate the value of at in the linear trend equation Ft k at btk while using double exponential smoothing O ataFt 1 alat 1 bt 1 O at B bt bt 1 1 B bt 1 O at B bt bt 1 1 y bt 1 O at aft 1 1 a at 1 bt 1

Suppose it is certain that an earthquake will occur someday What is the probability to the nearest percent that it will occur while you are at work Assume you are at work 9 hours per day 245 days p year Assume a 365 day year

Researchers wanted to study if couples having children are married They surveyed a large group of people The data are shown in the contingency table below What is the relative risk of being married for those who have children Round your answer to two decimal places Married Not Married Total Children No Children Total 97 35 132 68 71 139 165 106 271

A group of college freshman are targeted with a voter registration advertisement Another group of freshman are not targeted The table below shows how many of these freshman registered to vote What is the odds ratio for freshman targeted with the advertisement registering to vote against freshman not targeted with the advertisement registering to vote Round to two decimal places Targeted with advertisement Not targeted with advertisement Total Registered to vote Did not register to vote 103 78 181 36 64 100 Total 139 142 281

tors are testing a new antidepressant A group of patients all with similar characteristics take part in the study me of the patients receive the new drug while others receive the traditional drug During the study a number o ents complain about insomnia The data are shown in the contingency table below What is the relative risk of omnia for those who receive the new drug Round to two decimal places Insomnia No insomnia New drug Traditional drug 36 88 Total 52 226 295 521 Total 278 331 609 l

The matrix A det 2 a a11 a21 38 2 87 382 34 2 87 15 12 15 a12 922 34 A 87 a 34 2 b 0 which is the system a 2 The eigenvalue with positive imaginary part is For eigenvalue 2 the eigenvector v has components a and b that satisfy 38 a 15 b 0 where h i a 38 15 i 87 34 0 has characteristic equation b 0 b 0 Choosing the first component of the eigenvector as a 1 for 2 the eigenvector is a i

Researchers wanted to study if having a long beak is related to flight in birds They surveyed a total of 34 birds The data are shown in the contingency table below What is the relative risk of having long beaks for those birds that fly Round your answer to two decimal places Provide your answer below Long beak Not a long beak Total Flies Does not fly Total 11 3 14 8 12 20 19 15 34

A survey of 160 employed citizens was conducted and the results are shown in the table below Given that a randomly selected survey participant does not work in an office what is the probability that this person works on Saturday Provide your answer as a fraction Does not Work Saturday Works Saturday Total Provide your answer below Does not Work in an Office 21 5 26 Works in an Office 65 69 134 Total 86 74 160

Researchers wanted to study if wearing cotton clothes is related to depression They surveyed a large group of peopl he data are shown in the contingency table below What is the odds ratio for people wearing cotton clothes being epressed against people not wearing cotton clothes being depressed Round your answer to two decimal places Cotton Not cotton Total Depressed Not depressed 122 420 542 189 263 452 Total 311 683 994 E

A group of 130 students at a private university were asked if they are full time or part time and if they have gym memberships The results are shown in the table below Given that a randomly selected survey participant is part me what is the probability that this student has a gym membership No Gym Membership Gym Membership Total rovide your answer below Part time 13 5 18 Full time 59 53 112 Total 72 58 130

Alex wants to test the reliability of lie detector tests or polygraph tests He performs a polygraph test on a random sample of 12 individuals If there is more than a 50 chance that the tests result in no false positives that is the tes does not result in a true statement being recorded as a lie Alex will conclude that the tests are reliable If the probability of a lie detector test resulting in a false positive is 5 5 what will Alex conclude Use Excel to find the probability rounding to three decimal places Select the correct answer below O Alex will conclude that the test is reliable since the probability of no false positives is less than 0 5 Alex will conclude that the test is not reliable since the probability of no false positives is greater than 0 5 O Alex will conclude that the test is not reliable since the probability of no false positives is less than 0 5 O Alex will conclude that the test is reliable since the probability of no false positives is greater than 0 5 41

A roulette wheel has 38 slots numbered 1 to 36 and two green slots labeled 0 and 00 Jim a dealer at a roulette table tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands The ball has an equally likely chance of landing in each slot If Jim spins the ball around the wheel 25 times what is the probability that the ball lands in a green slot at most twice Use Excel to find the probability Round your answer to three decimal places

A basketball player has a 0 603 probability of making a free throw If the player shoots 28 free throws what is the probability that she makes no more than 20 of them Round your answer to 3 decimal places if necessary Provide your answer below

A softball pitcher has a 0 672 probability of throwing a strike for each pitch If the softball pitcher throws 15 pitches what is the probability that more than 9 of them are strikes Round your answer to three decimal places Provide your answer below P X 9

The probability of winning on an arcade game is 0 568 If you play the arcade game 22 times what is the probability of winning more than 15 times Round your answer to three decimal places Provide your answer below

Identify the parameters p and n in the following binomial distribution scenario A basketball player has a 0 511 probability of making a free throw and a 0 489 probability of missing If the player shoots 25 free throws we want know the probability that he makes no more than 10 of them Consider made free throws as successes in the binomial distribution Select the correct answer below O p 0 511 n 10 O p 0 511 n 25 O p 0 489 n 10 O p 0 489 n 25 111

Identify the option below that represents dependent events Select the correct answer below O rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw O rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two ro O drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a 3 and then rolling a 4 with a standard die

Identify the option below that represents mutually exclusive events Select the correct answer below drawing a red card and then drawing a black card with replacement from a standard deck of cards O rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two ro rolling a sum greater than 10 from two rolls of a standard die and rolling a 3 for the first roll drawing a 7 and then drawing another 7 with replacement from a standard deck of cards

A primary election is being held for a city to elect a new mayor Of the candidates 8 are Republicans 3 are third party candidates and 9 are Democrats If an independent voter randomly selects a candidate for mayor what is the probability that the candidate is third party Give your answer as a fraction

While commuting a driver sets her smartphone to randomly play songs from a pre selected list Of the songs on the list 6 are rock 5 are hip hop and 3 are country What is the probability that the first song played is rock Give your answer as a fraction

A bag contains 7 RED beads 10 BLUE beads and 3 GREEN beads If a single bead is picked at random what is the probability that the bead is RED Select the correct answer below OOO 10 20 13 20 7 20 17 20 20 TrendACY MORE INSTR

A deck of cards contains RED cards numbered 1 2 3 4 5 6 BLUE cards numbered 1 2 3 4 5 and GREEN cards numbered 1 2 3 4 If a single card is picked at random what is the probability that the card has an ODD number Select the correct answer below 10 HEEFT HE 15 8 15 14 15 6 15 2 15 15

A spinner contains the numbers 1 through 50 What is the probability that the spinner will land on a number that is not a multiple of 13 Give your answer as a fraction Provide your answer below

A deck of cards contains RED cards numbered 1 2 and BLUE cards numbered 1 2 3 4 5 Let R be the event of drawing a red card B the event of drawing a blue card E the event of drawing an even numbered card and Oth event of drawing an odd card Drawing the Blue 2 is an example of which of the following events Select all correct answers Select all that apply E BORO

A deck of cards contains RED cards numbered 1 2 3 4 5 6 and BLUE cards numbered 1 2 3 4 5 Let R be the event of drawing a red card B be the event of drawing a blue card E be the event of drawing an even numbered card and O be the event of drawing an odd card Drawing the Blue 3 is an example of which of the following events Select all that apply OB

Question A deck of cards contains RED cards numbered 1 2 3 4 5 and BLUE cards numbered 1 2 Let R be the event of drawing a red card B the event of drawing a blue card E the event of drawing an even numbered card and Othe event of drawing an odd card Drawing the Red 1 is one outcome of which of the following events Select all correct answers Select all that apply

If P A 0 34 and P A or B 0 71 which of the following is false O P A given B 34 if A and B are mutually exclusive OP A an B 191 if A and B are independent O P B 561 if A and B are independent OP B 37 if A and B are mutually exclusive OP B Cannot be determined if A and B are neither mutually exclusive nor independe

A random sample of the price of gasoline from 30 gas stations in a region gives the statistics below Complete parts a through y 3 89 s 0 25 a Find a 95 confidence interval for the mean price of regular gasoline in that region 3 797 3 983 Round to three decimal places as needed b Find the 90 confidence interval for the mean Round to three decimal places as needed

Which statement about the S3 method is incorrect The t test is an example of the method The plot data frame is an example of the method O It belongs to generic O The S3 methods are R functions they can be called directly

Poker is a common game in which players are dealt five cards from a deck of cards It can be shown that there are 2 598 960 different possible poker hands The winning hands from highest to lowest are shown in the table below Find the requested F Use a calculator Show your answer to nine decimal places P straight Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3 744 hands Flush 5 108 hands Straight 10 200 hands Three of a kind 54 912 hands Two pair 123 552 hands One pair 1 098 240 hands 444 20 WARHO V iv in

Suppose the probability of an event E is 0 20 Consider the process to find the odds in favor of this event Identify the following P E P E What are the odds in favor of this event

Suppose that you are testing the hypotheses Ho 16 vs HA 16 A sample of size 64 results in a sample mean of 15 5 and a sample standard deviauon of 2 a What is the standard error of the mean b What is the critical value of t for a 95 confidence interval c Construct a 95 confidence interval for u d Based on the confidence interval at a 0 025 can you reject Ho Explain a The standard error of the mean is 0 Type an integer or a decimal

company has 544 employees and 182 of them are college graduates Determine the proportion of all empinyees that are not college graduates 000 000

Use Newton s method to find all solutions of the equation correct to six decimal places 5 x 1 x 2x Ox 1 000000 x 0 887685 3 856974 x 0 799572 4 579117 x 0 000000 2 000000 x 0 345089 2 710644

Let A and B be events in a sample space S and let C S AU B Suppose P A 0 2 P B 0 5 and P A n B 0 1 Find each of the following a P AUB 0 6 b P C 0 4 c P AC 0 8 d P AC n BC 0 4 e P AC UBC 0 9 f P BC n C 103

A book claims that more hockey players are born in January through March than in October through December The following data show the number of players selected in a draft of new players for a hockey league according to their birth month Is there evidence to suggest that hockey players birthdates are not uniformly distributed throughout the year Use the level of significance a 0 01 Click the icon to view the table Click the icon to view the chi square table of critical values B Ho The distribution of hockey players birth months is uniformly distributed H The distribution of hockey players birth months is not uniformly distributed O C Ho The distribution of hockey players birth months is uniformly distributed H More hockey players are born in January March than October December O D Ho The distribution of hockey players birth months is not uniformly distributed H The distribution of hockey players birth months is uniformly distributed Compute the expected counts for each birth month The total number of hockey players is 174 Observed Count Expected Count 64 58 28 Birth Month January March April June July September October December 24 Round to two decimal places as needed

If the expected count of a category is less than 1 what can be done to the categories so that a goodness of fit test can still be performed Choose the correct answer below OA Two of the categories can be combined or the sample size can be increased OB The assumed probabilities can be adjusted so that none of the expected counts are less than 1 OC Nothing needs to be done The expected count can be approximated as 1 OD Nothing can be done The test cannot be performed

Explain why chi square goodness of fit tests are always right tailed Choose the correct answer below O A The chi square goodness of fit tests are always right tailed because negative values of the test statistic are important OB The chi square goodness of fit tests are always right tailed by convention A left tail test will always yield the same results OC The chi square goodness of fit tests are always right tailed because the chi square distribution is skewed to right O D The chi square goodness of fit tests are always right tailed because the numerator in the test statistic is squared making every test statistic other than a perfect fit positive

An environmental agency worries that many cars may be violating clean air emissions standards The agency hopes to check a sample of vehicles in order to estimate that percentage with a marg of error of 4 and 99 confidence To gauge the size of the problem the agency first picks 40 cars and finds 10 with faulty emissions systems How many should be sampled for a full investigatio The environmental agency should sample at least Round up to the nearest whole number vehicles

Determine the expected count for each outcome The expected count for outcome 1 is Round to two decimal places as needed n 594 i P 1 2 3 0 18 0 41 0 21 C