Probability Questions and Answers

A boy owns 6 pairs of pants 1 shirts 2 ties and 2 jackets How many different outfits can he wear to school if he must wear one of each item He can wear different outfits

Triomino s Pizza sells only pizza They offer three types of crust four types of cheese five meat toppings and seven vegetable toppings If you must order exactly one type of cheese one meat topping and one vegetable topping on your pizza how many different pizzas can you order at Triomino s Pizza

A random sample of 219 students were asked if they owned a pet or not The following contingency table gives the two way classification of their responses Own Pet 42 41 Male Female No Pet 65 71 Suppose one student is randomly selected from the group Calculate the following probabilities Round solutions to three decimal places if necessary P Female P Own Pet P Male Own Pet P No Pet Female

f a f a h f a h f a Need Help 0 25 Points Read It f a DETAILS SALGTRIG4 2 1 044 Find f a f a h and the difference quotient f a h f a where h 0 h f x 6x 5

14 De a Find the probability of randomly selecting a student who spent the money given that the student was given a 1 bill b Find the probability of randomly selecting a student who kept the money given that the stu dent was given a 1 bill What do the preceding results suggest

Question 15 continued f See the two 2 way tables below in which the data above are broken down by a third categorical variable which is the type of clinic A public or B private the subjects went to for treatments presented in percents Clinic A Outcome Success Failure Clinic B Treatment New 15 85 1 Existing public 5 95 Treatment New Outcome Success 95 Failure 5 Existing 50 50 private Is clinic a possible confounder for the association between Outcome and Treatment in this study What specifically in the tables shows this Yes the percent of the success failure

Answer Revenue 1000s 100 80 60 40 20 O T 1 Revenue of a Small Business 2 3 Month The y scale is too large for the given data The y scale is too small for the given data The y scale is appropriate for the given data

For 20 25 Use Table A Standard Normal Distribution to find the proportion of observations that satisfies each of the following statements In each case shade the area under the curve that is the answer to the question 20 23 3 2 1 0 z is less than 1 83 4 2 1 1 2 3 0 3 1 2 z is between 1 42 and 2 68 3 21 3 2 1 0 1 2 z is greater than 2 18 24 2 1 0 1 z is greater than 0 51 2 3 3 22 25 2 1 0 1 2 3 z is less than 0 33 3 2 1 0 1 2 3 z is between 2 and 1 53

A random process Y t has the power spectral density a Find the autocorrelation function of Y t b Find the average power in the process Y t Question 2 16 Syy W W 64 Let P 0 85 0 261 0 15 0 74 Hint P X X a Find stable probability matrix P

2 Let the function f x be defined by f 0 1 and f x for a 0 One can show that the function f is infinitely many times differentiable and that f equals to its Taylor series about x 0 Consider the function g t where a t e 1 a Then the power series representation of g t about t 0 is az t Write x y Write x y Write x y z Write e for e Write cos z for cos z parenthesis are required Write acos z for arccos z parenthesis are required Write In z if Inz parenthesis are required for for ay is required for and parenthesis are required I da

A company produces steel rods The lengths of the steel rods are normally distributed wi 262 2 cm and a standard deviation of 0 7 cm Answer the following to the nearest tenth of a cm Find P34 which is the length separating the shortest 34 rods from the longest 66 I rm

The table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Amelia s car over several months Miles Driven x Cost to Fill up y 292 Table U s Gas Fill Up Log 293 313 305 345 276 337 21 85 22 60 24 15 22 90 26 21 21 24 25 02 Copy Data Step 2 of 2 If Amelia needs to drive 311 miles home from college and leaves with a full tank how much should she budget to fill up when she gets home Assume the regression equation is appropriate for prediction Round your answer to the nearest cent

Solve the problem and find the equation Determine the type of conic section and sketch the graph 2 4 x 2 3 xy 2 y 10 3 x 10y 5

Years elapsed Total population billions Population 1 2 Year 11 10 9 4 3 2 1 World population milestones in billions 0 9 1804 1927 1959 1974 1987 1999 2011 2026 2042 123 32 13 12 12 15 16 T 2 billion 1928 15 7 billion 2010 6 billion 1998 O 5 billion 1986 3 billion 1959 4 billion 1973 O 9 billion 2037 8 billion 2022 1800 2022 estimates Median projection 80 prediction interval 95 prediction interval 1 What is the trend shown in time needed to add another billion to the human population 2 Why is causing the trend to behave the way it does 3 Identify describe 3 ways the trend in human population growth especially since the 1970s negatively affects marine populations

A Find the sample standard deviation rounding to one decimal place 5 9 13 7 15 5 14 7 10 OA 3 8 OB 12 9 C 14 5 OD 3 6

Suppose that percent offer is believed to be normally distributed with a mean of 0 30 and a standard deviation of 0 15 a What is the probability that a randomly selected person will offer at least 0 50 of their endowment I b What is the probability that a randomly selected person will offer less than 0 44 of their endowment c What is the probability that a randomly selected person will offer between 0 20 and 0 40 of their endowment

Suppose that to assign participants to their experimental condition the researchers used an 8 sided die where each number represents one of the eight different combinations of wealth and stakes Determine the expected value variance and standard deviation for the probability distribution of the random variable x where x is the outcome of the roll of an 8 sided die Provide a graph representing this probability distribution

a company needs new employees through an employee selection test from all test takers 20 of the participants pass a random sample 15 people Find the probability that there are exactly 5 participants and maximum of 3 people 7 40 02 AM

A coin operated drink machine was designed to discharge a mean of 7 fluid ounces of coffee per cup In a test of the machine the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded The sample mean and sample standard deviation were 7 08 fluid ounces and 0 25 fluid ounces respectively If we assume that the discharge amounts are approximately normally distributed is there enough evidence to conclude that the population mean discharge u differs from 7 fluid ounces Use the 0 10 level of significance Perform a two tailed test Then answer the questions below Carry your intermediate computations to three or more decimal places a State the null hypothesis Ho and the alternative hypothesis H Ho H b Determine the type of test statistic to use Z t Chi Square 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 conclude that the mean discharge differs from 7 fluid ounces Yes No

Given the data in the table what graph best de

Each year advertisers spend billions of dollars purchasing commercial time on network sports television In the first 6 months of 1988 advertisers spent 1 1 billion Who were the largest spenders A recent article listed the top 10 leading spenders in millions of dollars Calculate the sample variance rounding to two decimal places Company A 73 3 Company F Company B 62 9 Company G Company C 56 8 Company H 55 2 Company I 28 3 Company J Company D Company E OA 420 43 B 20 50 24 4 24 1 21 5 22 8 20 6 www

The following data represent the bachelor degrees of CEOs at area small businesses Determine the mode des Degree Number Accounting Business Liberal Arts Marketing Other A marketing B accounting C business P no mode 27 43 13 26 15

Eleven high school teachers were asked to give the number of students in their classes The sample data follows Would any of the class sizes be considered an outlier 36 31 30 31 20 19 24 34 21 28 24 No Yes

Multiple myeloma is a form of cancer Doctors surmise that t clinical trial 25 patients diagnosed as having multiple myelo recorded Suppose that the following histogram summarizes

Q3 8 If X N 0 find the density of Y X

1 Express in simplest radical form 8 x 6

Consider the given discrete probability distribution Find the probability that x exceeds 4 X p x 0 76 0 89 0 87 0 24 0 11 2 0 13 4 7 0 02 9 0 09

Find the mean of the given probability distribution 1 2 3 X 0 p x 0 26 0 11 0 16 2 42 2 26 02 2 16 2 52 4 0 42

A population of values has a normal distribution with 9 1 and o 43 7 You intend to draw a random sample of size n 97 Find P98 which is the score separating the bottom 98 scores from the top 2 scores P98 for single values Find P98 which is the mean separating the bottom 98 means from the top 2 means P98 for sample means Enter your answers as numbers accurate to 1 decimal place

Suppose that the distance of fly balls hit to the outfield in baseball is normally distributed with a mean of 244 feet and a standard deviation of 43 feet Use Onlinestatbook or GeoGebra to answer the following questions Write your answers in percent form Round your percentages to two decimal places a If one fly ball is randomly chosen from this distribution what is the probability that this ball traveled fewer than 192 feet P fewer than 192 feet b If one fly ball is randomly chosen from this distribution what is the probability that this ball traveled more than 222 feet P more than 222 feet

For a standard normal distribution find P 0 5 z 1 2 Question Help Post to forum

A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home improvement stores They select a simple random sample of 20 stores record how many of the flashlights were sold in a 30 day period and constructed a 95 confidence interval for the true mean number of flashlights sold a Explain what would happen to the width of the confidence interval if the confidence level were increased to 98 b How would we expect the width of the confidence interval to change if the flashlight manufacturer selected a much larger sample Explain c The 20 stores in the sample were actually the only stores who provided sales figures from 36 stores that were randomly chosen to be in the sample Can the manufacturer adjust the confidence interval to take this nonresponse into account If so how If not why not

The accompanying data represent the wait time in minutes for a random sample of forty visitors to an amusement park ride Complete parts a and b 6 8 22 0 16 47 6 2 3 10 9 20 9 5 5 5 32 29 12 3 29 7 6 0 26 6 10 54 9 15 7 22 9 0 6 3 9 30 14 7 14 a Determine and interpret the quartiles By the quartiles about of the wait times are Q minute s or less and about of the wait times exceed Q minute s about of the wait times are Q minute s about of the wait times are Q3 minute s Type integers or decimals Do not round minute s or less and about of the wait times exceed Q minute s or less and about of the wait times exceed Q3

A 2008 Gallup poll found that 47 of Americans felt that a third political party is needed to represent the American people In the description of methods the poll takers said For results based on the total sample of national adults one can say with 95 confidence that the maximum margin of sampling error is 3 percentage points You can safely conclude that Select one O a between 41 and 53 of all Americans think we should have a third party b 47 of all Americans think we should have a third party O c between 44 and 50 of all Americans think we should have a third party O d between 44 and 50 of the people interviewed think we should have a third party O e between 93 and 97 confident that 47 of all Americans think we should have a third party

A newspaper conducted a statewide survey concerning the race for state senator The newspaper selected a random sample of 1200 registered voters and found that 620 of them plan to vote for the Republican candidate Let p the true proportion of all registered voters in the state that plan to vote for the Republican candidate Which of the following gives the correct 90 confidence interval for p Select one O a 0 517 0 014 O b 0 517 0 022 O c 0 517 0 024 O d 0 517 0 028 O e 0 517 0 249

Other things being equal the margin of error of a confidence interval increases as the Select one O a sample size increases O b sample mean increases O c c O d O e none of the above confidence level increases confidence level decreases

A newspaper conducted a statewide survey concerning the Pennsylvania state senator race The newspaper selected a random sample of 1200 registered voters and found that 620 of them plan to vote for the Republican candidate Let p the true proportion of all registered voters in the state that plan to vote for the Republican candidate A 90 confidence interval for p is 0 517 0 024 There are about 8 million registered voters in Pennsylvania Based upon these data we can be 90 confident that the true number of registered voters in Pennsylvania that plan to vote for the Republican candidate is captured in the interval from Select one O a 3 944 million to 4 328 million voters O b 6 180 million to 9 920 million voters O c 4 133 million to 4 134 million voters O d 3 916 million to 4 432 million voters Oe 1 645 million to 1 960 million voters

nette must pass through three doors as she walks from her company s foyer to her office Each Which of the following describes the possible outcomes for whether Nanette encounters a locked L LLL UUU LLL LLU LUL LUU ULL ULU UUL UUU LLU LUL ULL UUL ULI O Non LUU

The probability that Peggy has math homew

17 Fast Food Drive Thru Accuracy If one order is selected find the probability of gettin order from McDonald s or Wendy s or an order that is not accurate The Accuracy If one order is selected find the probability of gettin b Assume an

b Assun 15 Fast Food Drive Thru Accuracy If two orders are selected find the probability that they are both accurate a Assume that the selections are made with replacement Are the events independent b Assume that the selections are made without replacement Are the events independent nd Drive Thru Accuracy If two orders are selected find the probability that they

9 Fast Food Drive Thru Accuracy If one food that is not from McDonald s 10 Fast Food Drive Thru Accuracy If one order is selected find the probability of getting an order that is not accurate order is selected find the probability of getting of selecting an ord

to identify the biggest mistakes that job candidates make during an interview there is a 50 50 18 Job Applicant Mistakes Based on an Adecco survey of hiring managers who were asked dney Smith wrote in On the Conduct of the Understanding that it is im chance that they will identify inappropriate attire ole of life

accurate and selecting an order from Wendy s 13 Fast Food Drive Thru Accuracy If two orders are selected find the probability that they are both from Taco Bell a Assume that the selections are made with replacement Are the events independent b Assume that the selections are made without replacement Are the events independent

that his or her luggage is black 16 Sleepwalking Based on a report in Neurology magazine 29 2 of survey respondents have sleepwalked 17 Randomness When using a computer to randomly generate the last digit of a phone num loot digit is zero

9 47 girls In Exercises 13 20 express the indicated degree of likelihood as a probability value between 0 and 1 13 Testing If you make a random guess for the answer to a true false test question there is a 50 50 chance of being correct to o multiple choice question on a

have sleep 17 Randomness When using a computer to randomly generate the last digit of a phone num ber to be called for a survey there is 1 chance in 10 that the last digit is zero

Order Accurate Order Not Accurate ol L McDonald s Burger King 329 33 264 54 249 145 31 pb10 13 a shift untrisha 10 Al 9 Fast Food Drive Thru Accuracy If one order is selected find the probability of getting food that is not from McDonald s n order is selected find the probability of getting

50 50 chance of being correct 14 SAT Test When making a random guess for an answer to a multiple choice question on an SAT test the possible answers are a b c d e so there is 1 chance in 5 of being correct Rased on a Harris noll if you randomly select a traveler there is a 43 chance

Using intervals of width 10 how many intervals are needed for this graph to be drawn correctly O 5 or fewer O between 6 and 10 O between 11 and 19 O 25 or more DONE 659 Number of Employees Fast Pax Number of Employees 12 Average Salary 39 500 0 19 Fast Pax Employee Salaries 20 29 30 39 40 49 50 99 100 199 200 29