Probability Questions and Answers

Find the range mean and interquartile range of each set of values 1 6 1 10 12 13 10 9 5 6 11 2 23 56 59 60 123 164 180 212 3 524 526 532 531 534 539 530 535 4 1 4 1 6 1 9 2 2 2 6 2 7 2 9 3 1 5 45 48 46 47 45 48 46 49 46 47 6 97 102 99 105 100 101 99 101 Know when to use S D X SX SAMPL u Ox population Mean Find the mean the standard deviation for each set of values to the nearest tenth 7 9 7 232 254 264 274 287 298 312 342 398

5 State Washington New York Louisiana Connecticut Kentucky Delaware Bachelor s Degree 31 32 4 21 4 35 6 21 28 7 8 x 36 Educational Attainment by US State Bachelor s Degree 29 9 21 8 30 5 35 7 29 2 State California Nevada Rhode Island Maryland Oregon State Florida Minnesota Calculate the z score for the following Given Mean 26 Stdev 4 6 x 12 7 x 29 Use the z score formula to find the missing value given the others 9 Find the mean given z 0 12 x 18 stvdy 3 Utah Texas Kansas Bachelor s Degree 25 3 31 5 28 5 25 5 29 5 10 Find the standard deviation given z 1 5 x 92 mean 105

The data below show the miles driven on a single day by a random sample of 14 students Calculate the 24th and 79th percentiles of the data P24 22 14 18 81 25 This means that approximately P79 This means that approximately Question Help Read 86 37 79 34 of the data lie below of the data lie below 26 78 64 89 60 when the data are ranked when the data are ranked

Data were collected for 461 sea turtles on the Treasure Coast The weight of the turtles in pounds is summarized in the table below Weight lbs 160 163 164 167 168 171 172 175 176 179 180 183 184 187 Frequency 86 88 48 34 91 What is the class boundary between the first and second classes Class boundary 28 86 What is the lower limit of the second class Lower Class Limit Midpoint What is the midpoint of the fourth class Upper Class Limit What is the upper limit of the fourth class

A data set consisting of newborn baby weights is normally distributed bell shaped with a mean of 8 5 pounds and standard deviation of 2 5 pounds Use the Empirical Rule to address the following questions Hint sketch the distribution to help visualize the problem Approximately 95 of the newborn weights lie between What approximate percentage of the newborn weights lie between 1 and 16 pounds and What approximate percentage of the newborn weights lie between 6 and 11 pounds de

Find the probability of picking 5 vowel s and 4 consonant s when 9 letters are picked with replacement from a set of alphabet tiles You may input your answer as a fraction or to the sixth decimal

The average new car price is 37000 with a standard deviation of 1850 Consider a random sample of 950 new cars Use Chebyshev s Rule to address the following questions Round solutions to the nearest whole number if necessary At least how many new car prices lie between 29600 and 44400 At least how many new car prices lie between 27750 and 46250

The following data are the amounts of total fat in grams in all sweet treats available at your local donut shop 16 22 18 17 16 17 23 18 17 16 Are these population or sample data Select an answer What is the range for this data set K What is the variance for this data set Round your answer to three decimal places if necessary What is the standard deviation for this data set Round your answer to three decimal places if necessary

A high school baseball player has a 0 314 batting average In one game he gets 6 at bats What is the probability he will get at least 3 hits in the game Round your answer to 4 decimal places

Given the function f x 4 f x solve for the following values If the value does no exist enter DNE lim f x x 0 lim f x x 0 f 0 x 0 4x 8 x 20

Which type of sampling method is being employed in the following example A post office manager was in charge of 11 postal delivery people He wanted to do a study on the customer s level of satisfaction for the customers he works with So he asked 3 of his delivery people to ask every person on their delivery route to rate their satisfaction of mail service on a scale of 1 to 10 Simple Random Sampling Stratified Sampling Cluster Sampling Sampling of Convenience F

If a seed is planted it has a 75 chance of growing into a healthy plant If 8 seeds are planted what is the probability that exactly 3 will grow Round your decimal to 4 places

Matching questions ask you to match each question on the left with one of the choices on the right Not a choices on the right may be used For the binomial distribution match each statistic with its formula n is the number of trials p is the probability of success BEE variance expected number of failures standard deviation mean or expected number of successes a np rounded to an integer b np C 1 1 d npq e nq f npq

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day Activities of dolphin 2013 The numbers in the table represent the number of groups of dolphins that were partaking in an activity at certain times of days Period Activity Morning Noon Afternoon Evening Total Traveling 6 6 13 39 Feeding 28 4 56 88 Socializing 38 5 10 62 Total 72 15 79 189 Round all of your answers to 4 decimal places What is the probability that a dolphin group is partaking in traveling P traveling 14 0 9 23 What is the probability that a dolphin group is around in the afternoon P afternoon What is the probability that a dolphin group is partaking in traveling given that it is afternoon P traveling afternoon What is the probability that a dolphin group is around in the afternoon given that it is partaking in socializing P afternoon socializing What is the probability that a dolphin group is around at noon given that it is partaking in feeding P noon feeding What is the probability that a dolphin group is around at noon and is partaking in feeding P noon and feeding What is the probability that a dolphin group is around at noon or is partaking in feeding P noon or feeding

Three hundred consumers were surveyed about a new brand of snack food Crunchies Their age groups and preferences are given in the table Liked Crunchies Disliked Crunchies No Preference Total 18 24 25 34 35 55 55 and over Total 66 118 12 22 89 160 167 300 5 3 35 43 23 6 13 42 24 1 23 48 One consumer from the survey is selected at random Round your decimals to 4 places What is the probability that the consumer is 18 24 years of age given that they dislike Crunchies What is the probability that the selected consumer dislikes Crunchies What is the probability that the selected consumer is 35 55 years old or likes Crunchies If the selected consumer is 70 years old what is the probability that they like Crunchies

A group of students were surveyed as to whether or not they had to complete chores at home at least once a week and whether they had a curfew Chores No Chores Total Fraction a What is the probability a student has a curfew if they have chores Fraction Curfew 13 12 25 Decimal rounded to 4 places b What is the probability a student has no curfew or has no chores Fraction No Curfew 5 3 8 Total 18 15 Decimal rounded to 4 places c What is the probability a student has a curfew and chores P chores Decimal rounded to 4 places d Are having chores and having a curfew independent O No because P chores is not equal to P chores given curfew OYes because the P chores is equal to the P chores given curfew Proof P chores given curfew

After giving a test below is the summary of grades by gender identity B C Total A Male 11 3 16 2 18 18 Female 9 15 Total 20 30 26 56 If a student is randomly chosen find the probability that the student identifies as male given they earned an A Enter your answer as a fraction It does not have to be reduced

A recent study surveyed 1 342 households asking if the residents rented or owned and if the residents included dependents The results are summarized below 1 or More Dependent No Dependents Total 184 628 Renter 337 714 Total 821 521 1 342 a What number of households reported having 1 or more dependent and renting Fill in the missing entry in the table Homeowner 444 b What percent of the renters reported having no dependents Round your percentage to 2 decimal places c Someone uses the table and calculates percent 184 521 35 32 Which is the correct interpretation of this O 35 32 of homeowners reporting having no dependents 35 32 of people with no dependents reported being homeowners O 35 32 of people surveyed were homeowners with no dependents O None of these are correct

Problem Solving Mathematical 1 Check for Reasonableness Write an equation with a letter for the unknown Then solve Check for reasonabl 5 The football team had its photo taken There are 3 rows of 8 players each The fourth row has 6 players How many players are in the team photo

Suppose that B1 and B2 are mutually exclusive and B2 is the complement event of B1 such that P B1 0 6 and P B2 0 4 Consider another event A such that P A B1 0 2 and P A B2 0 5 Find P A E 0 38 0 10 0 70 0 88 0 32

dx dt dy dt dz dt x t y t z t X1x X x X Y X2Y

Part 1 of 2 O Points 0 c e following table gives the counts for three price categories of 504 stocks in a Price Count 0 49 99 155 50 99 99 205 100 or higher 144 nd the probability that a stock in the portfolio is below 50 ow many stocks are below 50 stock s

gle fair eight sided die is rolled Find the probability of getting a robability is an integer or a simplified fraction O PAR

ose n ANB 7 n AUB 34 and n A 19 Use a diagram to determine n B

Solve Part 3 of 7 of dice is rolled Find the probability of rolling sum not more than 7 sum not less than 7 sum between 4 and 9 exclusive points Points 0 29 of 1 a How many possible outcom rolling two dice 36 Simplify your answer How many ways can two dice b their sum is not more than 7 21 Simplify your answer The probability of rolling a sum Type an integer or a simplified

en treated with an antibiotic 90 of all the dolphins are cured of an ea ted with antibiotics how many cured dolphins should be expected expected number of cured dolphins is und to two decimal places as needed

Points 0 of udy determined that 7 of children under 18 years old lived with their father only Find th children selected at random from 11 children under 18 years old lived with their father or probability that none of the children lived with their father only is not round until the final answer Then round to the nearest thousandth as needed

dom study reported that 74 of very low birth weight babies graduate from high school ow birth weight babies are followed through high school how many would you expect to ol O Points 0 of 2 LIK umber of very low birth weight babies expected to graduate is lify your answer

Solve the following matrix equation then select the answer that provides in the correct order the values of x x2 and x3 8 2 11 x1 7 3 2 5 X2 4 2 12 5 X3 2 1 368 1 059 0 3849 0 5628 1 176 1 280 1 176 0 5628 1 280 0 3849 1 059 1 368

Convert the following system of linear equations into matrix form Ax b where x x x x3 for b 2 10 017 Then select the answer that provides the value of the first row second column element of the matrix A OOO The first row second column does not exist S494 7x1 4x2 2x3 10 X 3x x3 0 x 5x3 2 00

Perform the matrix multiplication below then select the answer that provides the value of the resultant matrix element in the third row first column 0 1 15 6 1 2 0 1 2 5 10 The third row first column does not exist 1 25 5 1 0 21 0

Select the answer that provides the z component of the Cartesian vector 101 8k 10 0 8 10

Given two Cartesian vectors 111 24j k 1 20j k 71 8j 13k 1 81 11k 31 8 k and and 2 1 3k select the answer that provides the vector i 4

Select the answer that provides the determinant of the following 3x3 matrix 5 0 5 7 61 20j 35k 61 201 35k 61 20j 35k 6 20j 35k 61 20j 35k k 2 4

Select the answer that provides the dot product 2 of the Cartesian vectors 101 10j k and 3 4k 69 26 301 4k 30x 4z

Select the answer that provides the unit vector in the same direction as the Cartesian vector 2 j k 0 81651 0 4082 0 4082k 0 33331 0 1667J 0 1667k 0 51 0 25j 0 25k 081651 0 40821 040826

Select all X 185 5 2012 2 299 values that satisfy the following equation 0 5

nancial services committee had 60 members of which 9 were women If 8 memb probability that the group of 8 would be composed as the following men and 3 women men and 2 women at least one woman The probability that the group will consist of 5 men and 3 women is 0771 und to four decimal places as needed The probability that the group will consist of 6 men and 2 women is 2534 und to four decimal places as needed How can the probability that the group will consist of at least one woman be found A P at least one woman 1 P at least one man B P at least one woman 1 P all men C P at least one woman 1 P all men D P at least one woman 1 P at least one man probability that the group will consist of at least one woman is und to four decimal places as needed

Part 3 of 3 A car dealership has 6 red 14 silver and 5 black cars on the lot Ten cars are of the dealership Complete parts a through c below a Find the probability that 4 cars are red and the rest are silver 0 0138 Round to four decimal places as needed b Find the probability that 5 cars are red and 5 are black 000002 Round to six decimal places as needed c Find the probability that exactly 6 cars are red Points Round to five decimal places as needed

lue Question 13 9 1 37 BE points O Points 0 of 2 An insurance company has written 100 policies for 75 000 500 policies for 60 000 and 1000 p for people of age 20 If experience shows that the probability that a person will die at age 20 is 0 the company expect to pay out during the year the policies were written The company can expect to pay out over the year after the policies were written Type an integer or a decimal

ipment of 8 computers contains 2 with defects Find the probability that a sample of size contain a defective computer t is the probability that a sample of 4 of the 8 computers will not contain a defective com Type an integer or a simplified fraction

unts adio station runs a promotion at an auto show with a money box with 15 100 tickets ets The box contains an additional 20 dummy tickets with no value Find the probabi chosen probability that three 100 prizes are chosen is und to five decimal places as needed

shipment of 11 computers contains 2 with defects Find the probability th Il not contain a defective computer e probability is ype an integer or a simplified fraction

Question 11 8 5 31 BE 12 study asked respondents about their dence in banks and financial institutions ell as their confidence in major orations Each question allowed three Onses a great deal only some or hardly The table to the right summarizes the onses Find the probability a respondent a great deal of confidence in banks and cial institutions given that he or she has y any confidence in major corporations Confidence in Banks and Financial Institutions A Great Deal Only Some Hardly Any Total HW Score 10 2 of 20 points O Points 0 of 1 Confidence in Major Corporations A Great Only Hardly Deal Some Any 69 123 23 Total 141 662 288 183 494 1297 59 465 13 74 215 812 270 robability a respondent has a great deal of confidence in banks and financial institutions given th ardly any confidence in major corporations is nd to four decimal places as needed

Question 15 8 5 39 LS able shows frequencies for red green color ess where M represents person is male and C sents person is color blind Use this table to find 1 4 Round to three decimal places as needed HW Score 50 10 o O Points 0 of 1 M M 0 045 0 4 C C 0 366 0 5 Totals 0 411 0 5

the table shows the result of a restaurant survey Meals Service good Service poor Total Lunch 62 Dinner 40 Total 32 18 50 30 22 52 102 O Points 0 nd the probability the service was good given that the meal was dinner he probability the service was good given that the meal was dinner is ype an integer or a simplified fraction

12 You roll two dice Let A roll a three on either die and let B roll a sum greater than or equal to 8 What is the P A a 0 3333 b 0 2556 c 0 4167 d 0 3056 e 0 2290 13 You roll two dice Let A roll a three on either die and let B roll a sum greater than or equal to 8 What is the P A or B a 0 6111 b 0 7222 c 0 1111 d 0 5873 e 0 6785

FRQ Three students are randomly selected by the Vice Principal from a group of 10 student council members There are 6 seniors and 4 juniors of the student council Three seniors are selected A What is the probability that random selection would result in three seniors being chosen B Design a simulation for this selection process using the partial table of random digits that is presented below Clearly describe all of the steps in your simulation process C Use the partial table of random digits presented below and carry out 10 trials of your simulation Clearly present your results What is the probability of obtaining three seniors based on your simulation 11354 48721 32089 51823 00349 38632 48855 21081 76150 98125 46712 09274 D Based on your simulation results do you have convincing evidence that the Vice Principal did not randomly choose the three students from the student council Explain

e multiplication principle to solve e improvement store website listed 220 different of glass wall tile 34 colors of acrylic grout 25 kinds tar trowels and 27 different kinds of mortar How ways are there to buy the products needed for a tile There are needed

aluate C mplify your answer Type an integer or a fraction