Probability Questions and Answers

The table shows some trees that are in two city parks Let U be the smallest possible set that includes all the trees listed R be the set of trees in Riverside Park and S be the set of trees in Sleepy Hollow Park Find SnR Use the lowercase letters in the table to list the elements in SnR SNR Use a comma to separate answers as needed Sleepy Hollow Park Riverside Park Aspen a Oak o Willow w Birch b Oak o Dogwood d Maple m Aspen a Pine p Willow w

Today the waves are crashing onto the beach every 4 seconds The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4 seconds Round to 4 decimal places where possible a The mean of this distribution is b The standard deviation is c The probability that wave will crash onto the beach exactly 3 7 seconds after the person arrives is P x 3 7 d The probability that the wave will crash onto the beach between 1 5 and 3 6 seconds after the person arrives is P 1 5 x 3 6 e The probability that it will take longer than 1 seconds for the wave to crash onto the beach after the person arrives is P x 1 f Suppose that the person has already been standing at the shoreline for 0 7 seconds without a wave crashing in Find the probability that it will take between 2 3 and 3 6 seconds for the wave to crash onto the shoreline g 61 of the time a person will wait at least how long before the wave crashes in h Find the maximum for the lower quartile seconds seconds

Based on your results above which of the correlations is stronger The correlation between lifeexpectancy and fertility rate or The correlation between lifeexpectancy and internet users per 100 people O The correlation between life expectancy and fertility rate O The correlation between life expectancy and internet users per 100 people O They are equal in size O Impossible to determine

During one shift the express lane clerk recorded how many times customers violated the 10 items or less rule for his lane In particular he recorded how many items over the limit each violator placed on the conveyor belt This data is summarized in the histogram below NOTE The last class actually represents 7 or more items not just 7 items Frequency 14 12 10 8 4 2 05 15 25 35 45 5 5 65 75 items over 10 Q What is the frequency of times the limit was exceeded by more than 6 items Answer times

59 17 Seved Calculate the gross pay for the following employee an apple picker assuming she picked 7 200 apples Rate per Apple Number of Apples 1 2 000 2 001 3 000 0 07 0 08 Over 3 000 0 12 Gross pay

In a study the sample is chosen by dividing all students into groups then randomly selecting 3 of the groups What is the sampling method Systematic Convenience 29999 Simple random Stratified Cluster

0 2 58 18 Calculate maturity value for the interest bearing note using ordinary interest Note Round your answer to the nearest cent Discount Rate 13N Face Value 42 000 Maturity value Time in Days 79

Top Select all that apply U 43 Using the interquartile range which of the following are outliers Select all correct answers 44 48 40 64 69 72 79 86

D op A deck of cards contains red cards numbered 1 2 3 4 5 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 red 1 is an example of which of the following events Select all correct answers Select all that apply RORE B Ih

DD QUESTION 24 1 POINT Which of the pairs of events below is dependent Select the correct answer below drawing a 2 and drawing a 4 with replacement from a standard deck of cards O rolling two 4 s from two rolls of a standard die O drawing a heart and drawing another heart with replacement from a standard deck of cards drawing a face card and then drawing a 3 without replacement from a standard deck of cards

QUESTION 23 1 POINT A deck of cards contains red cards numbered 1 2 3 4 5 6 blue cards numbered 1 2 and green cards numbered 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 If a single card is picked at random what is the probability that the card is blue Give your answer as a fraction Provide your answer below

What is the missing relative frequency Number of Movies 0 1 2 3 4 5 6 7 8 9 10 or more Relative Frequency 0 08 0 20 0 30 0 10 0 08

Data Value Relative Frequency Cumulative Relative Frequency 1 2 3 4 0 19 0 18 0 30 0 33 100

A purchasing manager at a university is investigating which brand of LCD projector to purchase for equipping classrooms Of major concern to her is the lifetime of the light bulbs used in the projectors One company has published the following histogram regarding the lifetimes of a sample of 50 bulbs used in its LCD projectors Frequency 15 11 Carlton 7 15 10 5 700 4 750 800 850 Bulb lifetime in hours 900 9 950 4 1000 Based on the histogram find the proportion of bulb lifetimes in the sample that are less than 950 hours Write your answer as a decimal and do not round your answer Aa V

Below are the line plots for two data sets 2 Mean of data set A XX Mean of data set B Data set A 4 X X X X 5 XX 6 XX Find the mean of each data set 8 7 9 09 X 9 XX 1 X XXm 2 Data set B XX X 4 5 6 7 8 9 E

The following are distances in miles traveled to the workplace by 18 employees of a certain computer company 7 2 37 32 27 22 16 11 6 1 15 15 10 10 10 5 5 5 Send data to calculator Draw the histogram for these data using an initial class boundary of 0 5 an ending class boundary of 45 5 and 5 classes of equal width Note that you can add or remove classes from the figure Label each class with its endpoints Frequency 8 7 6 5 0 0 0 0 0 00 00 0 X

A real number between 2 and 7 will be picked according to the probability distribution shown in the figure Regions under the curve are labeled with A B and C The area of each region is shown in the table 0 1 2 3 B 4 5 6 7 8 a Find the probability that a real number between 3 and 5 is picked 0 Region A B C Use the figure and the table to answer the parts below b Find the probability that a real number between 3 and 7 is picked 0 Area 0 12 0 56 0 32 E

Click the icon to view the closing prices data Date 09 03 2010 09 07 2010 09 08 2010 09 09 2010 09 10 2010 09 13 2010 09 14 2010 09 15 2010 09 16 2010 101 100 Stocks and the stock exchange over 12 days Complete parts a through c a Use Excel s Data Analysis Exponential Smoothing tool to forecast each of the stock prices using simple exponential smoothing with a smoothing constant of 0 3 Complete the exponential smoothing forecast model for stock A Type integers or decimals rounded to two decimal places as needed Forecast A 30 17 2010 GELDE Closing Prices Stock Exchange C 10 536 56 10 245 77 Date A B C 09 03 2010 127 07 18 54 20 84 09 07 2010 124 84 18 21 20 45 09 08 2010 125 67 17 77 20 83 09 09 2010 126 46 17 95 20 56 09 10 2010 126 88 18 01 20 73 09 13 2010 128 77 18 66 21 13 09 14 2010 129 34 18 71 21 46 D 15 44 15 55 15 72 10 320 11 15 92 10 490 35 16 01 10 384 72 16 13 10 558 58 16 21 10 609 24 09 15 2010 128 41 18 74 21 43 16 33 09 16 2010 129 12 18 84 21 89 16 37 10 485 36 10 508 38 X 4

XI 9 Type an integer or a decimal Do not round

Chapter 11 K Express the following probability If one person is selected

What is the probability of obtainin

Questi etermine whether the following statement is true BIA is the probability that event B occurs if the Choose the correct answer below

11 Determine whether the following statemen Probability problems with the word or in

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 76 inches and a standard deviation of 10 inches What is the probability that the mea annual precipitation during 25 randomly picked years will be less than 78 8 inches Round you answer to four decimal places A 0 0808 B 0 4192 OC 0 5808 D 0 9192

A group consists of five Democrats and a In how many ways can four peopl b In how many ways can four Repu c Find the probability that the select

pter 11 K A group consists of five Democrats a In how many ways can four

Questi a Larry Tyrone and Sergio have all been in

er 11 K The table shows the number expressed in millions of citizens w

Which formula can be used to find the probability of two forward steps in a biased random walk beginning at location 0 given ten total steps and the probability of a forward step is 0 3 OP 2 x 0 3 0 7 8 101 21 8 OP 2 x0 3 0 7 8 OP 2 x 0 3 0 7 OP 2 x 0 32 0 7

A gymnast is standing at point O She does a front tuck one movement forward each time a head is flipped and a back tuck one movement backward each time a tail is flipped What is the probability of one forward movement given three total movements and a probability of 0 5 for taking a step in either direction OO 0 375 0 5

A chip is placed at point 0 on a number line What is the probability of seven movements to the right in a biased random walk given ten total movements and the probability of a right movement is 0 25 0 0 003 O 0 12 0 0 5

Which formula can you use to find the probability of arriving at a certain location using a biased random walk OP k p 1 p n k OP k k p 1 p k OP k nk p 1 p k OP k n Pkx p 1 p k

Start at point 0 on a number line What is the probability of five movements to the right in a random walk given five total movements and a probability of 0 5 for taking a step in either direction 00 0 03125 00 33

A coach pulls the goalie because the team scored a goal when she did so in the first game What is the error in the coach s reasoning too small of a sample confirmation bias Odata does not support decision data does not apply to decision

To get the ball back quickly in basketball a coach decides to have one of his players foul a player on the opposing team which gives the opposing team an opportunity to attempt a foul shot and score a point Opposing player A makes 1 10 of the foul shots B makes 3 10 C makes 5 10 and D makes 2 10 Which player should the team foul O Opposing Player A OOpposing Player B OOpposing Player C

After a touchdown the kicker of a football team makes a one point conversion 90 of the time The team makes a two point conversion 40 of the time Should the coach decide to make a one point conversion or two point conversion O one point conversion because the expected outcome is lower O one point conversion because the expected outcome is greater O two point conversion because the expected outcome is lower two point conversion because the expected outcome is greater

Which is an example of decision making based on confirmation bias instead of statistics OA baseball coach believes a runner on the field will advance any time a batter bunts The last six times the baseball coach asked a batter to bunt a runner on the field advanced bases one time The coach has the next batter bunt to advance the runner on the field OA baseball coach believes a runner on the field will advance any time a batter bunts The last six times the baseball coach asked a batter to bunt a runner on the field advanced bases each time The coach has the next batter bunt to advance the runner on the field OA baseball coach believes a runner on the field will advance any time a batter bunts The last six times the baseball coach asked a batter to bunt a runner on the field advanced bases five times The coach has the next batter bunt to advance the runner on the field A baseball coach believes a runner on the field will advance any time a batter bunts The last six times the baseball coach asked a batter to bunt a runner on the field advanced bases four times The coach has the next batter bunt to advance the runner on the field

A baseball runner has successfully stolen a base six out of the last eleven attempts Should the coach have him attempt to steal on this attempt OYes six out of eleven bases means there is more than a 50 chance to steal the base OYes eight bases means there is more than a 50 chance to steal the base O No six out of eleven bases means there is less than a 50 chance to steal the base No bases cannot be stolen

In the last minute of the game a soccer coach knows that she has an 80 chance of scoring a goal if she pulls her goalie How did the coach make her decision Odata O confirmation bias O coin toss

Out of the eight times the baseball coach asked a batter to bunt a runner on the field advanced bases two times What is the probability that a player will advance given this data 0 0 25 0 5

Express 3 32 9 43 in interval notation COM Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals Do not round OA The interval is OB The interval is

Let 7 21 represent an interval on the number line Complete parts a and b below www a Find the value that is in the middle of the interval The value is Type an integer or a decimal Do not round

If 0 777 0 999 is an interval on the number line find the value that is in the middle of the interval The value is Type an integer or a decimal Do not round

This information would be MOST useful to which of the following government departments Mean travel time to work minutes workers age 16 years 2012 2016 26 1 Department of Transportation Department of Commerce Department of Education

The data depicted in this graph would be of most use to which of the following federal departments Doctorate recipients thousands 25 20 15 10 5 Female S E fields Department of Labor Male S E fields O Department of the Interior Female non S E fields 0 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Department of Education Male non S E fields

The graph below is part of the publication Dietary Guidelines 2015 2020 Which statement correctly interprets the data presented Cup Equivalents 3 2 5 2 1 5 0 5 0 Fruits Recommended Intake Ranges Males years 31 50 51 70 71 3 2 5 2 1 5 0 5 O Average Intake 9 13 14 18 19 30 Des Source What We Eat in America NHANES 2007 2010 O Males between 19 to 50 years of age on average eat less than the recommended amount of fruit O No age group eats the recommended amount of fruit O Women between 51 and 70 years of age on average eat more fruit than recommended 31 50 Females years 51 70 2 71

The figure below is from the Centers for Disease Control and Prevention Which statement correctly interprets the dat presented Percent Age Adjusted Prevalence of High LDL Cholesterol Among Adults Aged 40 74 by Sex and Age United States 1976 1980 to 2007 2010 80 70 60 50 40 30 20 10 27 1976 1980 1908 1904 2001 2004 2007 2010 31 Total Ages 40 64 Ages 65 74 Men Women Sostkamuung Inerted p 0 05 NOTES High LDL chords mesured ve above the bestment que estoshed by the National Choward Education Programs Adult Teement Pa pudenes Estimates are age added by the suctmetot to the US cnis population using age groups 40 64 and 65 74 Souros COCACS Nato His and Button Examination Survey 2010 Gaynon Inc O Men tend to have higher cholesterol levels than women The standard deviation for the cholesterol level of men is greater than the standard deviation of women O Cholesterol levels tend to decrease as people reach their 60s and 70s K

File Edit Go CONTENTS Tools Help Section 4 An Extended Exploration The t Test Isle Royale is meaningful if the probability of it occurring by chance alone its p value is less than 0 05 How do you obtain a p value Given the value of t and something called the degrees of freedom in your data you can determine the p value using a handy dandy t test p value calculator The number of degrees of freedom in your t test is equal to the total number of samples 12 in this case minus 2

Assume that the United States economy is currently in a short run equilibrium with the actual unemployment rate above the natural rate of unemployment a Draw a single correctly labeled graph with both the long run Phillips curve and short run Phillips curve Label the current short run equilibrium point P b Assuming no policy actions are taken will the short run Phillips curve shift to the right upward shift to the left downward or remain the same in the long run Explain

Worldwide experts estimate that 107 males are born for every 100 females Express this as a ratio of males to females as a decimal 1 07 107 O 0 107 10 7