Probability Questions and Answers

2 What is the probability of hitting a bull s eye on a target with a dart if in the long run 71 c of every 489 attempts actually hit the bull s eye

CO Suppose the percent of the total work force that is female is given by p t 0 0035t 0 47t 34 where t is the number of years past 1970 a Graph the function y p t 70 60 50 40 y 30 20 10 y 70 60 50 40 RO 50 100 150 t 200 70 60 50 40 30 201 10 30 webassign net 100 150

A deck of cards has 13 cards per suit in four suits clubs spades hearts diamonds For each question below assume a full deck that is well shuffled 1 What is the probability of drawing any club 2 What is the probability of drawing any two 3 What is the probability of drawing a queen of hearts

Two Way Frequency Tables MC Students at a virtual school are allowed to sign up for one math class each year The numbers of students signing up for various math classes for the next school year are given in the following table Grade Geometry Algebra II Pre Calculus AP Statistics 10th 20 7 10 3 0 7 11th 6 7 12th 1 4 Total 29 13 8 6 7 31 3 4 10 3 13 8 27 6 2 8 9 12 4 Total 35 2 33 8 31 1 What did the student actually calculate and what is the correct answer A student calculated the joint relative frequency of 10th grade students in geometry as being 71 4 The student calculated the conditional relative frequency for students who are in 10th grade given that they are enrolled in Geometry The correct value of the joint relative frequency of 10th grade students in geometry is 20 7 The student calculated the conditional relative frequency for students who are in 10th grade given that they are enrolled in Geometry The correct value of the joint relative frequency of 10th grade students in geometry is 29 The correct value of the joint relative frequency of 10th grade students in geometry is 20 7 The student calculated the marginal relative frequency for 10th grade students in geometry The student calculated the marginal relative frequency for 10th grade students in geometry The correct value of the joint relative frequency of 10th grade students in geometry is 29 O

a random sample of 100 items an or equal to 0 44 probability will be nd to four decimal places as n

a When n 4 and 0 19 P X 0 L Round to four decimal places as needed b When n 10 and x 0 30 P X 9 Round to four decimal places as needed c When n 10 and 0 60 P X 8 Round to four decimal places as needed d When n 3 and 0 88 P X 2 Round to four decimal places as needed

n K Question 7 of 19 Given a standardized normal distribution with a mean of 0 and a standard deviation of 1 determ a P Z 1 05 b P Z 0 24 c P 1 96 Z 0 24 d What is the value of Z if only 21 19 of all possible Z values are larger Click here to view page 1 of the cumulative standardized normal distribution ble Click here to view page 2 of the cumulative standardized normal distribution table a P Z 1 05 Round to four decimal places as needed b P Z 0 24 Round to four decimal places as needed c P 1 96 Z 0 24 Round to four decimal places as needed d Z Round to two decimal places as needed

Exam K Use the contingency table below to find the p a A B b AB d Are events A and B independent a P A B b P A B c P A B Round to two decimal places Round to two decimal places Round to two decimal places

A manufacturer makes bags of popcorn and bags of potato chips The average w 0 02 ounces The average weight of a bag of potato chips is supposed to be 5 08 a bag of popcorn from the assembly line and it has a weight of 3 06 ounces Ther weight of 5 03 ounces Which description closely matches the findings on the ass Answer The popcorn bag assembly line is closer to the specifications give assembly line

Linear Functions Fit to Data LC A student believes there is a correlation between the number of texts sent during class and GPA The student collected data and found that the line of fit can be modeled by the equation Identify and interpret the slope in this scenario The slope is 3 9 Starting at 0 1 the GPA will increase by 3 9 for every text sent in class The slope is 3 9 Starting at 0 1 the GP will decrease by 3 9 for every text sent in class O The slope is 0 1 Starting at 3 9 the GPA will increase by 0 1 for every text sent in class O The slope is 0 1 Starting at 3 9 the GPA will decrease by 0 1 for every text sent in class 3 9 0 1 x

Weighted Averages MC Use the table to answer the question that follows ROR Portfolio 1 Portfolio 2 Portfolio 3 7 3 1 150 1 100 1 8 1 825 525 6 7 1 405 825 10 4 1 045 400 2 7 1 450 800 2 500 250 1 200 1 880 2 225 Using technology calculate the weighted mean of the RORS for each portfolio Portfolio 3 Portfolio 1 Portfolio 20 Portfolio 2 Portfolio 3 Portfolio 10 Portfolio 1 Portfolio 2 Portfolio 30 Portfolio 3 Portfolio 2 Portfolio 10 Based on the results which list shows a comparison of the overall performance of the portfolios from to worst best

Test Midterm Exam stion list estion 1 stion 2 jon 3 n 4 K Results of a 2017 survey of a sample of executives from 175 banks r importance is boosting profitability and identifying growth areas Fifty mobile app relationship management MARM solution was ranked a greatest anticipated strategy to enhance the customer experience C A the 175 executives representing bank institutions OB the 98 bank institutions in the region that note mobile app exp OC all bank executives OD the 72 bank institutions in the region OE the 72 bank institutions in the region that cite mobile app ban c What is a possible parameter of interest

Exam K A government agency reported the given sources of electricity in a particular area in 2010 a Construct a Pareto chart b What percentage of power is derived from coal nuclear or natural gas c Construct a pie chart d For these data is it better to use a Pareto chart or the pie chart Why a Choose the correct chart below A 100 EB D C A Source OB Question 11 of 19 100 0 CD BE Source Q Q 12

3 2 Please state and verify if the following state G can be reached or not from state S in Problem A B and C respectively 341 1 2 3 A 25 8 7 6 State S C 4 8 12 4 5 6 4 7 8 State G 1 2 3 5 6 7 9 10 11 15 13 14 State S B 2 3 4 5 1 7 State S 1 LO 5 68 9 13 2 3 4 6 7 8 10 11 12 15 14 State G 1 2 3 4 5 6 8 7 State G

Find the probability of 3 successes in 3 trials if the probability of success on each trial 50 8 2

The time taken to calibrate an instrument to characterize samples in the lab is a random variable having a norm distribution of 20 minutes and a standard deviation of 2 minutes What is the probability that an instrument can calibrated in a period of time 4 1 less than 19 5 minutes 2 2 between 20 and 22 minutes 2

Question 10 Multiple Choice Worth 1 points Linear Functions Fit to Data MC The graph shows a scatter plot for a set of data Length cm 4 3 5 3 2 5 2 1 5 0 5 1 0 0 5 O 1 31x 0 02 Determine the equation for a line of fit for the data O 1 31x 0 02 Oy 0 82x 1 98 1 O 0 82x 1 98 1 5 Width cm 2 2 5 3

A restaurant manager recorded the number of people in different age groups who attended their food festival They created the following histogram Number of People 60 50 40 30 20 10 0 20 What percentage of the participants are ages 40 to 59 Round to the nearest whole percent 35 O 60 Food Festival Participants 0 19 20 39 40 59 60 79 Age Group yr 4000

According to a leasing firm s reports the mean number of miles driven annually in its leased cars is 12 860 miles with a standard deviation of 3100 miles The company recently starting using new contracts which require customers to have the cars serviced at their own expense The company s owner believes the mean number of miles driven annually under the new contracts is less than 12 860 miles He takes a random sample of 12 cars under the new contracts The cars in the sample had a mean of 11 329 annual miles driven Assume that the population is normally distributed Is there support for the claim at the 0 01 level of significance that the population mean number of miles driven annually by cars under the new contracts is less than 12 860 miles Assume that the population standard deviation of miles driven annually was not affected by the change to the contracts Perform a one tailed test Then answer the questions below Carry your intermediate computations to three or more decimal places and round your responses as specified below a State the null hypothesis Ho and the alternative hypothesis H 0 Ho H b Determine the type of test statistic to use Z t Chi Square 4 F Degrees of freedom if applicable c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places e Can we support the claim that the population mean number of miles driven annually by cars under the new contracts is less than 12 860 miles Yes

Last month Walmart surveyed 3000 customers to find out w one month

Indicate the level of measurement for Answer

1 point What is the probability First Choice of selecting BA Second Choice Outcome Probability AA AB BA

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips The mean shopping time spent by customers at the supermarkets has been reported to be 38 minutes but executives have good reason to believe that is greater than 38 minutes The executives hire a statistical consultant and ask her to perform a statistical test To perform her statistical test the consultant collects a random sample of shopping times at the supermarkets She computes the mean of these times to be 42 minutes and the standard deviation of the times to be 10 minutes Based on this information complete the parts below a What are the null hypothesis Ho and the alternative hypothesis H that should be used for the test Ho H b Suppose that the consultant decides to reject the null hypothesis What sort of error might she be making Type 1 Type II c Suppose the true mean shopping time spent by customers at the supermarkets is 45 minutes Fill in the blanks to describe a Type II error A Type II error would be rejecting failing to reject the hypothesis that is than less than or equal to greater than greater than or equal to not equal to equal to 10 38 42 when in fact is than 42 greater than 38 less equal to 10 equal to 38 less than 10 less than 38 less

perpetuity interest rate 2 2 calculation The Idealistic Insurance Company offers a perpetuity which pays annual payments of 50 000 This contract sells for 1 500 000 toc What is the interest rate O 0 97 O 31 30 3

The 1995 payroll amounts for all major league baseball teams are shown below According to the graph what percent of payrolls were within the 30 million 39 milli range Frequency 12 10 8 10 ST N 1995 Payroll of Baseball Teams rounded to the nearest million dollar 10 Select one O a 8 O b 42 1 O c 18 5 20 30 Millions of Dollarc 8 50

Which measure of dispersion is not resistant to extreme values in a data set Select all that apply Select one or more O a range O b Interquartile Range IQR O c variance O d standard deviation

The circle graph shows the results of the student council presidential election Who got the most votes Student Council President 600 total votes Lili 35 Select one O a Ted O b Lili c Jim Ted 30 Matt 20 Jim 15

For the data below construct a frequency distribution using five classes Describe th shape of the distribution The data set ages of 20 cars randomly selected in a stude parking lot 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1 Select one O a skewed to the left O b symmetric O c skewed to the right Od uniform

The grade point averages of 10 students are listed below Find the range of the da 0 8 2 0 1 8 2 9 0 9 4 0 3 3 2 9 3 6 3 2 Select one O a 3 2 Ob 2 8 OC 2 4 Od 14

A student scores 56 on a geography test and 258 on a mathematics test The geography test has a mean of 80 and a standard deviation of 20 The mathematics test has a me of 300 and a standard deviation of 28 If the data for both tests are normally distributed on which test did the student score better relatively speaking Select one O a We must know the number of students in the class to do the required calculations O b The student scored the same on both tests O C The student scored better on the mathematics test O d The student scored better of the geography test

ww to 2 4 to k 16 Macmillan Learning now to HOW W To help consumers make informed decisions hospitals A large regional hospital and a sma patients in critical condition because of its sta hospital specializes in scheduled surgeries an The counts of patients who survived surgery performed in the previous year The regional weeks after surgery for both patients admitte

nment Score ion 5 of 18 2 4 Stacked M D A study compared the success rates of two different nephrolithotomy PCNL a minimally invasive tech removing patients kidney stones by type of procedu stones and for patients with large stones Small stones Success Failure Open surgery 81 6 PO To access the complete data set click the link for you Excel Minitab14 18 Minitab18 JMP SPSS TI

Assignment Score 2 4 Question 2 of 18 U Side Peanut alle Western co peanuts fir raising the recommen infants wit assigned t consume p

selected find the following probabilities using GeoGebra Note when you use GeoGebra write down what you are entering to show your work The way we define a binomial variable is X Binomial n p and fill in the numbers you entered for n and p That way I can give you partial credit accordingly if something goes wrong a What is the probability that exactly 8 of them have brown eyes b What is the probability that at least 12 of them have brown eyes c What is the probability that at most 6 of them have brown eyes d How many of them do we expect to have brown eyes With what standard deviation Include

Answer each of the following questions completely There is a total of 15 points possible in the assignment 1 7 pts The table below gives the grades for MTH 243 for all students at all PCC campuses for the 2011 2012 academic year Note that Southeast did not become a full campus until 2014 Write a final answer in sentence form with the result as a percent rounded to two decimal places i e 23 45 A B C D P F NP W Incomp Audit 334 292 182 83 14 80 123 4 141 106 67 25 9 24 42 3 282 185 128 42 3 77 71 1 757 583 377 150 26 181 236 8 For all questions ask yourself what is the chance or likelihood if you randomly select one Statistics student at PCC from the 2011 2012 academic year a What is the probability they had an A given they were attending Cascade campus Sylvania Cascade Rock Creek Total 1112 417 789 2318 b What is the probability they were attending Sylvania given they withdrew W from the class c Are the two events campus and grade independent Show mathematical proof

Washing Machine Microwave Dishwasher Washing M Microw Drye

A small commuter airline keeps records of comp

O Points model of the car you are thinking of buying is available in five different col y ways can the car be ordered Ow many ways can the car be ordered

A small commuter airline keeps records of complaints receive complaints are due to the categories Plane often late or Poor r

Question 50 9 4 13 GI n is tossed 5 times Find the probability that all are heads probability that all are heads is nd to three decimal places as needed Fr

ine 0 32 0 41 0 54 0 45 0 46 Stem tenths 3L 3H 4L 4H SL SH 6L 6H anc gravity values 7L 7H 0 35 0 36 0 36 0 37 0 38 0 40 0 41 0 42 0 42 0 42 0 42 0 46 Construct a stem and leaf display using repeated stems Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values various 0 47 0 48 0 48 Leaf hundredths 0 42 0 49 used in 0 40 0 40 0 43 0 44 0 51 0 54 0 55 0 58 0 61 0 66 0 66 0 67 0 68 0 78 Comment on any interesting features of the display Select all that apply There is a small amount of variation in the data The data value 0 78 is a possible outlier The stem and leaf display shows that 0 45 is a good representative value for the data The display is not symmetric and appears to be positively skewed The display is symmetric The data value 0 32 is a possible outlier The stem and leaf display shows that 0 55 is a good representative value for the data

Select all x values that satisfy the following equation 2x x 11x 10 0000 2 2 5 2 10 2 5 1 1 10

business journal reports that the probability that Internet users in the United States will use a mobile payment app is 0 60 The journal claims this indicates that out of 5 randomly selected cernet users 3 will use the mobile payment app the business journal interpreting the probability correctly A No because the Internet users are not independent of each other B C D No because only 60 of all people use the Internet No because 0 60 represents probability in the long run for many Internet users Yes because Internet users are selected at random

1 A 55 slug mass is supported by two cables AC and BC The magnitudes of the tensions in cables AC and BC are 7 651 kN and 5 818 kN respectively Define the origin of the Cartesian coordinate system at point C Write the weight force W and the two tension forces TCA and TCB as Cartesian force vectors using the metric system of units SI 46 TCA 24 TCB 55 slugs

How many different committees can be formed from 6 teachers and 37 students if the committee consists of 3 teachers and 4 students points O Points 0 of 1 Save In how many ways can the committee of 7 members be selected

A number between 1 and 10 inclusive is randomly chosen Events A B C and D are defined as follows A The number is even B The number is less than 7 C The number is less than or equal to 7 D The number is 5 Identify one pair of independent events Hint P A and B P A P B if and only if A and B are independent events A and C A and D B and D A and B B and C

Weighted Averages MC An investment portfolio is shown below Investment Money Market Account 3 200 1 750 1 235 2 300 Government Bond Preferred Stock Common Stock O 0 5 O 1 1 Amount Invested ROR 2 1 O 2 3 Using technology calculate the difference between the arithmetic average ROR and the weighted average ROR Round to the nearest tenth of a percent O 3 5 4 4 7 8 10 5

Two Way Frequency Tables MC A sample of 50 high school and college students were surveyed to choose a favorite free time activity playing sports dancing or watching movies TV 40 of the sample is high school students From the sample it is found that 22 were high school students who chose playing sports and 6 were high school students who chose dancing 10 were college students who chose sports and 18 were college students who chose watching movies TV 38 of the students surveyed chose dancing Which of the following is a correct two way relative frequency table for the data O High School and College Student Leisure Time Activity Preferences Sports Dancing Movies TV Row Totals 0 40 0 60 High school students 0 22 College students Column totals 0 10 0 32 0 32 0 38 High school students 0 11 0 03 College students 0 05 0 16 Column totals 0 16 0 19 0 06 High school students 11 College students Column totals O High School and College Student Leisure Time Activity Preferences Sports Dancing Movies TV Row Totals 0 40 3 16 5 16 38 High school students 22 College students 10 Column totals 32 6 32 38 0 18 0 30 0 12 0 06 0 09 O High School and College Student Leisure Time Activity Preferences Sports Dancing Movies TV Row Totals 0 15 6 9 30 1 12 18 0 60 O High School and College Student Leisure Time Activity Preferences Sports Dancing Movies TV Row Totals 40 30 1 20 30 50 60 100

Let P Z 0 43 P Y 0 42 and P Zn 0 18 Use a Venn diagram to find a P ZnY b P Z UY c P Z UY and d P ZnY a P Z ny 33 Type an integer or a decimal b P Z UY 82 Type an integer or a decimal e P ZUY 25 Type an integer or a decimal CHES

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