Probability Questions and Answers

od and food In a study of the effects of mood on evaluation of nutritious food 208 subjects were ran domly assigned to read either a happy story to induce a positive mood or a control no story neutral mood group Subjects were then asked to evaluate their atti tude toward a certain indulgent food on a nine point scale with higher numbers indicating a more positive attitude toward the food The following table summa rizes data on the attitude rating 14 Group Positive mood Neutral mood n 104 104 X S 4 30 2 05 5 50 1 74 a What are the standard errors of the sample means of the two groups b What degrees of freedom does the conservative Op tion 2 use for two sample t procedures for these data c Test the null hypothesis of no difference between the two group means against the two sided alterna

11 Weeds among the Corn Lamb s quarter is a common weed that interferes with the growth of corn An agriculture researcher planted corn at the same rate in 16 small plots of ground then weeded the plots by hand to allow a fixed number of lamb s quarter plants to grow in each meter of corn row No other weeds were allowed to grow Here are the yields of corn bushels per acre for only the experimental plots controlled to have one weed per meter of row and nine weeds per meter of row WDCORN One weed meter 166 2 157 3 166 7 161 1 Nine weeds meter 162 8 142 4 162 8 162 4 Explain carefully why a two sample t confidence interval for the difference in

3 Smart Watch Battery Life To check the lifetime of a new battery in a soon to be released smart watch with GPS an engineer used the GPS tracking fea ture of the watch continuously beginning with a fully charged battery until the battery was drained The engineer repeated this for a total of 10 times He compared the results with the lifetime of 4 8 hours for the current battery used in the company s GPS enabled smart watch

1 1 Smartphones and Spouses Choose a random sample of 100 married couples Ask each member of the couple how much time they spend looking at their smartphone while at home Compare the mean times for the two mem bers of couples

1 According to the records of an auto insurance company the average distance that their customers drive to work is 17 4 miles You are a new agent and you think this is too low You do a random polling of 50 of the company s customers and you find that the average is 18 5 miles with a standard deviation of 3 4 miles Do these data provide enough evidence at the 0 05 level of significance to conclude that the average distance driven to work is actually more than 17 4 miles a 1 pt State the null and alternative hypotheses b 1 pt State the p value c 1 pt What is your conclusion about the null hypothesis d 2 pts What is your conclusion in context of this problem

Find the slope of the line y 8 x 10 Write your answer as an integer or as a simplified proper or improper fraction

Complete the process of solving the equation Fill in the missing term on each line Simplify any fractions 3y 1 1 3y y Subtract 1 from both sides Divide both sides by 3

Find the y intercept of the line y 8 13 Write your answer as an integer or as a simplified proper or improper fraction not as an ordered pair

Here is a sample data set 533 1 619 9 541 2 526 6 434 6 526 6 478 6 539 3 534 4 505 5 431 2 613 4 471 5 541 3 444 6 533 7 468 8 451 9 405 7 538 3 528 9 451 1 549 3 418 2 468 8 518 1 495 8 544 1 468 539 3 631 485 5 483 5 468 8 536 8 472 1 539 1 539 3 608 8 617 7 492 9 509 8 458 1 536 3 531 3 405 4 606 6 526 7 534 2 626 8 440 3 459 6 617 8 500 6 Find the first quartile for this data set Q Find the third quartile for this data set Q3 Find the interquartile range for this data set IQR

The percent distribution of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old is shown in the pie chart Find each probability a Randomly selecting a mother 30 39 years old P 30 to 39 b Randomly selecting a mother not 30 39 years old P not 30 to 39 Round to the nearest thousandth as needed c Randomly selecting a mother less than 45 years old P less than 45 Round to the nearest thousandth as needed d Randomly selecting a mother at least 20 years old P at least 20 Round to the nearest thousandth as needed Round to the nearest thousandth as needed SOCCE Number of Multiple Births 00 15 19 1 6 20 24 6 3 25 29 21 3 30 34 37 3 35 39 24 6 40 44 5 3 45 54 3 6

The 81 th percentile of lightbulb lifespan is 1500 hours What does this mean of light bulbs have a lifespan of less than or equal to 1500 hours 06 CH

A set of data items is normally distributed with a mean of 112 and a standard deviation of 15 Convert each of the following data items to a z score Round your answer to the nearest hundredth a 212 Z b 94 Z

A standard deck of cards contains 52 cards One card is selected from the deck a Compute the probability of randomly selecting a club or diamond b Compute the probability of randomly selecting a club or diamond or heart c Compute the probability of randomly selecting a king or club a P club or diamond Round to three decimal places as needed b P club or diamond or heart Round to three decimal places as needed c P king or club Round to three decimal places as needed

4 different color dice are rolled and the numbers showing are recorded How many different outcomes are possible Your answer is

The Venn diagram here shows the cardinality of each set Use this to find the probability of observing the given set A 5 C 6 7 2 14 8 9 B 4

A jar contains 5 red marbles numbered 1 to 5 and 10 blue marbles numbered 1 to 10 A marble is drawn at random from the jar Find the probability that the marble is red or odd numbered

In how many different ways can a police department arrange a lineup if each lineup contains 8 people

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories Smooth Rhythm Standard The results were then presented to the owner in the following Venn Diagram Smooth 5 12 15 Standard 6 Rhythm 7 14 a Q If a student is chosen at random what is the probability that Write your answers in percent form Round to the nearest tenth of a percent a The student has competed in none of the categories b The student has competed in all three of these categories c The student has competed in Smooth or Standard but not Rhythm d The student has competed in Rhythm and Standard but not Smooth e The student has competed in Rhythm

A girl has 8 skirts 9 blouses and 9 pairs of shoes How many different skirt blouse shoe outfits can she wear Assume that each item matches all the others so she is willing to wear any combination Your answer is

In the 6 51 lottery game a player picks six numbers from 1 to 51 How many different choices does the player have Your answer is

Suppose a designer has a palette of 6 colors to work with and wants to design a flag with 3 vertical stripes all of different colors How many possible flags can be created

In how many ways can 3 students from a class of 15 be chosen for a field trip Your answer is

How many ways can 8 candles be arranged on a shelf

Let P U 0 28 and P V 0 28 and P V 0 47 Events U and V are mutually exclusive Find P U or V O 1 6785714285714 O 0 59574468085106 O 0 75 O 0 1316 O 0 19 O 0 19

With a population of 3500 people we randomly sample 139 people without replacement Is it reasonable to assume that the trials are sampled independently O No because the sample size is greater than or equal to 5 of the population size O No because the sample size is less than 5 of the population size O Yes because the sample size is less than 5 of the population size OYes because the sample size is greater than or equal to 5 of the population rito

than percents In a family with 5 children what is the probability of having 3 boys and then 2 girls in that order Exclude multiple births and assume all outcomes are equally likely In a family with 5 children what is the probability of having 3 boys and 2 girls in any order Exclude multiple births and assume all outcomes are equally likely

The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 52 while 36 require a developmental math course and 30 require a developmental English course Find the probability that a first year student requires both a development math course and a developmental English course

You own 15 CDs You want to randomly arrange 7 of them in a CD rack What is the probability that the ra ends up in alphabetical order The probability that the CDs are in alphabetical order is

A pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces How many different recital programs are possible

Compute the value of

Find the value of 7 P3 O 5 040 O 24 0 210 35

A restaurant offers a choice of 6 salads 12 main courses and 7 desserts How many possible 3 course meals are there

Standard automobile license plates in a country display 2 numbers followed by 3 letters followed by 2 numbers How many different standard plates are possible in this system Assume repetitions of letters and numbers are allowed Your answer is

A die is rolled twice What is the probability of showing a 1 on the first roll and an even number on the second roll Your answer is

A survey of 138 persons was conducted at TCC and it was found that 10 persons carried a cell phone 97 persons carried a tablet computer and 7 carried both a cell phone and a tablet 1 How many people carried a cell phone or a tablet 2 How many people carried neither a cell phone nor a tablet 3 How many people carried a cell phone only 4 How many people carried a tablet but not a cell phone

A survey asks Which online services have you used in the last month Twitter Facebook Have used both The results show 33 of those surveyed have used Twitter 59 have used Facebook and 8 have used both What percent of the people surveyed used neither Twitter nor Facebook

An urn contains 7 blue 5 yellow and 3 gray marbles Two marbles are randomly drawn from the urn Find the probability the two marbles are the same color O 83 225 O 68 225 O 68 210 03040

Suppose you roll a special 7 sided die What is the probability that the number rolled is a 1 OR a 2

c Assume that the class has 80 students and that the examination period is 130 minutes in length How many students do you expect will be unable to complete the exam in the allotted time Before finding the number of students who will be unable to complete the exam in 130 minutes first find the probability that any student does not complete the exam in 130 minutes If the student does not finish the exam in the first 130 minutes then it will take more than 130 minutes to complete As a probability statement completing the exam in more than 130 minutes is P x 7130 First convert the random variable x 130 to a normal random variable z Recall that the mean was given to be 100 minutes and the standard deviation was given to be a 20 minutes Z x O 130 100

89 Salaries for managers in a restaurant chain are normally distributed with a mean of 44 000 and a standard deviation of 6 500 We randomly survey 10 managers from that district a Find the 90th percentile for an individual manager s salary b Find the 90th percentile for the average manager s salary

Using the standard normal z random variable the probability statement P 60 x 85 is now P 2 z 0 75 so the normal probability table can be used The area to the left of 2 is Select than the area to the left of 0 75 Therefore the probability of P 2 z 0 75 will be calculated as Select The area under the curve to the left of z 2 was found to be 0 0228 Use the table excerpt below to find the area under the curve to the left of z 0 75 P Z 0 75 to four decim places 0 00 0 2119 0 2420 0 2743 Z 0 8 0 7 0 6 P Z 0 75 0 01 0 2090 0 2389 0 2709 0 02 0 2061 0 2358 0 2676 0 06 0 07 0 08 1949 0 1922 0 1894 0 05 0 1977 0 2266 0 2236 0 2206 0 2177 0 2578 0 2483 0 2546 0 2514 0 03 0 2033 0 04 0 2005 0 2296 0 2327 0 2611 0 2643 0 09 0 1867 0 2148 0 2451

45 of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder Among Latino California registered voters 57 5 prefer life in prison without parole over the death penalty for a person convicted of first degree murder 36 3 of all Californians are Latino These preferences are summarized in the contingency table below Latino 0 25875 0 10425 0 363 Total 0 45 0 55 1 Suppose that one Californian is randomly selected Let C represent Prefer Life Sentence and I represent Latino Round your answers to parts a and b to two decimal places a What is P C Prefer Life Sentence Prefer Death Penalty Total Non Latino 0 19125 0 44575 0 637 b What is P CL c Are C and L independent events O Yes because P C and P CIL are equal O No because P C and P CIL are not equal

The desired probability is P 60 x 85 First convert this probability statement using the standard random variable z Recall the formula for this conversion below where x is the value that needs to be converted is the population mean and o is the population standard deviation Z We found the z value that corresponds to x 60 to be z 2 Find the z value that corresponds to x 85 with mean 100 and standard deviation o 20 x x 0 6 85 100

The probability statement was determined to be P z 0 14 Recall that the normal probability table gives the area under the curve to the left of a given z value An excerpt is given below Z 0 00 0 01 0 02 0 03 0 04 0 0 0 5000 0 5040 0 5080 0 5120 0 5160 0 05 0 06 0 07 0 1 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 2 0 5793 0 5832 0 5871 0 5910 0 08 0 5199 0 5239 0 5279 0 5319 0 09 0 5359 0 5675 0 5714 0 5753 0 5948 0 5987 0 6026 0 6064 0 6103 0 6141 Use the above table to find the probability of completing the exam in an hour or less P z 0 14 rounding the result to four decimal places P z 0 14

The correct size of a nickel is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each income group who drew the nickel too small and too large Low Income High Income Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from the low income group that drew the nickel too large is b The proportion of children from the high income group that drew the nickel too large is c The proportion of all children that drew the nickel too large is d If a child is picked at random what is the probability they are in the low income group given they drew the nickel too large e If a child is picked at random what is the probability they are in the high income group OR drew the

The correct size of a certain object is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each group who drew the certain object too small and too large Group 1 Group 2 Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from group 1 that drew the object too large is b The proportion of children from group 2 that drew the object too large is c The proportion of all children that drew the object too large is d If a child is picked at random what is the probability they are in group 1 given they drew the object too large e If a child is picked at random what is the probability they are in group 2 OR drew the object too large

Phi Delta Kappa PDK is an international professional organization for educators that in collaboration with Gallup has been conducting polls on the public s attitudes toward the public schools since 1969 The following was one of the questions on the most recent poll conducted June 4 13 2011 Most teachers in the nation now belong to unions or associations that bargain over salaries working conditions and the like Has unionization in your opinion helped hurt or made no difference in the quality of public school education in the United States The respondents answers broken down by party affiliation is shown below Republican Democrat Independent Helped Hurt 35 197 52 6 Made no difference Don t know refused Which of the following statements is correct 146 78 105 12 69 178 90 4 O A histogram or a box plot would be useful to investigate if distribution of opinion on teachers belonging to unions or bargaining associations varies by political party affiliation O The results of the survey suggest a relationship between opinion on teachers belonging to unions or bargaining associations and political party affiliation O 14 of Republicans and 58 of Democrats think that teachers belonging to unions or bargaining associations helped the quality of public school education in the United States O The results of the survey suggest that opinion on teachers belonging to unions or bargaining associations and political party affiliation are independent

Every cereal box has a gift inside but you cannot tell from the outside what the gift is The store manager assures you that 13 of the 60 boxes on the shelf have the secret decoder ring The other 47 boxes on the shelf have a different gift inside If you randomly select two boxes of cereal from the shelf to purchase what is the probability that BOTH of them have the secret decoder ring Give answer as a decimal correct to four decimal places probability

Giving a test to a group of students the grades and shirt colors are summarized below A B Red Shirt 19 3 Blue Shirt 14 2 C Total 35 33 68 13 17 Total 17 21 30 If one student is chosen at random a Find the probability that the student has a Red Shirt GIVEN they got a C Round to 4 decimal places if needed b Find the probability that the student got a C GIVEN they are wearing a Red Shirt Round to 4 decimal places if needed

Write the given number using prime factorization Write your answer using Exponential Notation For instance 98 2 7 2 Instructions Find the prime factorization of 6