Probability Questions and Answers

grade for a statistics student are given What is the student s weighted mean score The student s weighted mean score is 91 50 Simplify your answer Round to two decimal places as needed W Homework Quiz Quiz Project Final Exam Score Percent 88 85 98 95 88

You plan to take a 1905 mile trip in your car which averages 30 miles per gallon How many gallons of gasoline should you expect to use Would a car that has only half the gas mileage require twice as much gasoline for the same trip Explain You should expect to use about Type an integer or a decimal gallons of gasoline

Find the following Probabilities given 500 people were surveyed Total Sports a b C Men Women Total Dance 0 04 0 32 0 36 0 20 0 12 0 32 TV 0 16 0 16 0 32 0 40 0 60 1 00 That a person surveyed does not dance That a woman surveyed likes sports How many people surveyed were men who liked dance

Opening Activity In a class of 30 students 3 out of the 16 girls and 6 out of the 14 boys are left handed Draw a Venn diagram and find the probability that a student chosen at random is a boy or left handed L 3 6 B 8 13

f 4 2 f x 0 for x 4 f 4 0 and f x 0 for x 4 fiction that has the properties described below Choose the correct graph below O A Ay 4 2 B 4 2 57 Next question O C D

function as the composition of two functions y 14 6x Choose the correct answer below OA If f x 1 1 x and g x 14 6x then y f g x 1 OB If f x x and g x then y f g x 14 6x OC If f x x and g x 14 6x then y f g x OD If f x and g x 14 6x then y f g x

y 24x16x 9 given function Next question This test 20 points pembin This question 1 points pomm The x intercept s is are Type an ordered pair Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression

O y x 2 x 8x 1 Choose the correct setup below to differentiate the function O d y x 2 x 2 x 8x 1 dx d dx O y x 2 x 8x 1 x 8x 1 x 2 dx dx x 8x 1 y 2 x 2 x 2 2 x 8x 1 dx d x 2 2 x 8x 1 x 8x 1 dx d y x 2 x x 1 x 2 dx y x 2 x 8x 1 x 8x 1 x 2

Which of the functions below are increasing for all x B I 1 t Q This test 20 point s possible This question 1 point s possible A Submit tes Select the correct choice below and if necessary fill in the answer box to comple choice Type A B C or D Use a comma to separate answers as needed OB None of the functions are increasing for all x

f x x 1 2 x 5 function has one relative extreme point Find it and determine whether it is a relative maximum or a relative minimum The relative extreme point is Type an ordered pair Is the relative extreme point a relative maximum or a relative minimum Relative maximum Relative minimum 1 point s po

K Find the derivative of the function 9x 7 y 8x 3 The solution is y 0

Allie buys a box of granola bars to hand out to her friends at school There are twelve granola bars in the box in which six are chocolate chip three are raisin and three a peanut butter Allie randomly passes out the granola bars to her friends Determine whether each statement indicates the correct probability for the occurrence of events as described Select Yes or No for each statement AB C The probability that the first two friends both get chocolate chip is 0 250 The probability that the first friend gets peanut butter and the second friend gets chocolate chip is 0 136 The probability that the first friend gets raisin and the second friend gets peanut butter is 0 063 Yes 00 No

13 Two marbles are drawn from a bag containing 11 red 10 white and 9 purple What is the probability of drawing Red first purple second 1 red and 1 purple No white marbles Same color DRAG DROP THE ANSWER 11 X 30 29 30 II 30 10 XXNSE 10 9 y 8 X X 29 30 29 X x 2 29 20 19 30 29 II 9 30 29

Suppose you spin the spinner one time AA 15 U a B A D A BA Probability C A D Construct a probability model Outcomes D B B C b What is the probability of the spinner not landing on ar

8 A coin is tossed and a die is rolled What is the probability that the coin shows tails and the die shows a multiple of 2 Leave your answer in fraction form

10 Kylie has a collection of bows for her hair She has two different sizes small and large All the bows are either solid or have a pattern Small Pattern 8 Solid 7 Large 6 7 What is the probability as a percentage that a randomly selected bow is large and has a pattern Enter your answer rounded to the nearest whole number in the space provided 06

Place an X In the table to show whether each pair of events is mutually exclusive or inclusive A person is 27 years old and 29 years old A student is walking and listening to music A number is even and is a multiple of 5 A number is odd and is a multiple of 2

2 a Noah surveyed 500 sophomores and juniors about their third period classes His results are summarized in the relative frequency tab Math Science History Total 0 24 0 20 0 68 0 08 0 15 0 32 0 32 0 35 1 00 Sophomore 0 24 0 09 0 33 Junior Total Part A What is the probability that a surveyed student does not have third period history b Part B What is the probability that a surveyed junior has third period math c Part C How many surveyed students are sophomores with third period science

A card is picked from the following cards Find the probability that the card drawn is purple Answer Note Use slash to separate numerator and denominator

Part 3 of 4 102 points O Points 0 of 1 Save Another useful measure of variation for a data set is the mean absolute X deviation MAD It is calculated by the formula MAD a Find the mean absolute deviation of the data set here Compare the result b The mean absolute deviation of the data is X

Determine whether the given value is a statistic or a parameter A sample of 50 patients is selected from among the patients admitted to the emergency room at a hospital and it is found that 28 have no health insurance O Statistic O Parameter

Find the mean of the data summarized in the given frequency table The highway speeds of 100 cars are summarized in the frequency table below Find the mean speed Highways Speeds of Cars Speed mph Cars 3 30 39 40 49 50 59 60 69 70 79 58 9 mi h O 56 1 mi h O 61 7 mi h 18 51 16 12

23 A survey was conducted among office workers regarding if their preferences on coffee versus soda The Venn diagram below represents the responses Survey of Office Workers Drinks Coffee Drinks Soda 31 12 25 83 Find the following probabilities as a fraction do not simplify P Coffee only P S P CUS P CS

A total of 200 people attend a party as shown in the table A person is selected at random to win a prize The probability of selecting a female is 0 6 The probability of selecting a child given that the person is a female is 0 25 The probability of selec a male given that the person is a child is 0 4 Complete the two way table to show the number of adults children males and females who attended the party Male Female TOTAL Adults 150 Children 50 TOTAL 80 120 200

22 The probability that the event A occurs is 3 is the probability that A occurs given that B occurs Answer Note Use slash to separate numerator from denominator the probability that event B occurs is 5 8 and the probability that events A and B both occur is 9

21 At Kennedy Middle School the probability that a student takes Technology and Spanish is 0 087 The probability that a student takes Technology is 0 68 What is the probability that a student takes Spanish given that the student is taking Technology Type your result in the empty box provided below in decimal form rounded to the hundredth place Answer

What is the sum of the first nine terms of the given geometric series 6 24 96 384

B You pick a card at random from the following cards put it back and then pick another card at random Find P blue blue Write your result in th empty box provided below Answer into numerator and denominator

17 In a class of 25 students 3 2 of the class are boys of the class have blonde hair and of the class are boys with blonde hair 5 If one student is to be chosen at random from the class what is the probability that the student is a boy or has blonde hair Show your work on the scratchpad P boy or blonde hair

5 The probability that event A occurs is 7 A and B both occur Write your result in the empty box provided below in a simplest fraction form P A and B Note Use slash to separate numerator and denominator 2 and the probability that event B occurs is If A and B are independent events what is the probability that 3

Given P A 0 20 P B 0 70 P BIA 0 55 and P A B 0 16 which statement is correct about events A and B A is the complement of B B A and B are independent events A and B are dependent events DB is the complement of A

Find the sum of the series 7n 17 n 1

4 What is the summation formula for the series below 4 8 16 32 2048 10 B 10 C 4 4n 6 2 4 1 n 1 10 2n 6 n 1 10 4 2 n 1 n 1

340 340 310 320 310 360 350 330 260 380 340 320 310 360 350 330 ake a dotplot of these data type Dotplot ow boxplot 260 270 280 290 300 310 320 330 340 350 360 370 Calories per Serving alain what the dot above 260 represents 380

State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Dist of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Med 1985 1996 2002 70 4 71 0 73 5 61 2 62 9 67 3 64 7 62 0 65 9 66 6 66 6 70 2 54 2 55 0 58 0 63 6 64 5 69 1 69 0 69 0 716 70 3 71 5 75 6 37 4 40 4 44 1 67 2 67 1 68 7 62 7 69 3 71 7 51 0 50 6 57 4 71 0 71 4 73 0 60 6 68 2 Bus 3 7 Soc State 33 31 19 25 23 27 11 9 29 3 17 9 2 5 8 2 9 1 3 3 34 The following data are the resting pulse rates for 30 randomly selected individuals who were participants at a 10K race Montana Nebraska Nevada COST 49 40 59 56 55 70 49 59 55 49 58 54 56 55 65 57 61 41 52 60 49 57 3 35 Consumer Reports in its May 1998 issue provides cost per daily feeding for 28 brands of dry dog food and 23 brands of canned dog food Using the Minitab computer program the following side by side boxplot for these data was created 3 5 3 0 2 5 2 0 1 5 1 0 5 0 a Construct a stem and leaf plot of the pulse rates b Construct a boxplot of the pulse rates c Describe the shape of the distribution of the pulse rates d The boxplot provides information about the distribution of pulse rates for what population DOG FOOD COSTS BY TYPE OF FOOD New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming 3 10 The following table presents homeownership rates in percentages by state for the years 1985 1996 and 2002 These values represent the proportion of homes owned by the occupant to the total number of occupied homes CAN TYPE a From these graphs determine the median lower quartile and upper quartile for the daily costs of both dry and canned dog food b Comment on the similarities and differences in the distributions of daily costs for the two types of dog food Summarizing Data from More Than One Variable Graphs and Correlation 70 2 67 6 74 2 75 0 69 9 72 8 73 9 68 3 67 5 70 2 Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri 68 5 73 2 73 5 70 2 64 9 67 1 73 7 76 5 73 9 65 6 66 9 72 0 60 5 61 7 62 7 70 7 73 3 76 0 70 0 75 4 77 3 69 6 73 0 74 8 69 2 70 2 74 6 Source U S Bureau of the Census http www census gov ftp pub hhes www hvs html 3 36 For the homeownership rates given in Exercise 3 10 construct separate boxplots for the years 1985 1996 and 2002 1985 66 5 68 6 68 5 66 8 57 0 61 1 65 5 65 0 62 3 64 6 68 2 67 1 70 3 50 3 68 0 52 7 55 0 70 4 70 0 69 5 69 9 68 2 67 9 69 2 72 0 69 4 70 5 68 4 61 5 63 1 66 2 56 6 59 6 71 6 71 7 74 0 61 4 72 0 72 9 77 3 67 6 67 8 71 5 67 6 68 8 70 1 60 5 61 8 63 8 71 5 72 7 72 7 69 5 70 2 70 3 68 5 74 3 68 5 66 8 63 1 67 0 75 9 74 3 77 0 63 8 68 2 72 0 73 2 68 0 72 8 b What major differences exist among the plots for the three years c Why do you think the plots have changed over these 17 years 1996 2002 69 3 68 4 54 55 72 51 46 55 63 55 DRY 65 5 69 5 67 2 a Construct relative frequency histogram plots for the homeownership data given in the table for the years 1985 1996 and 2002 d How could Congress use the information in these plots for writing tax laws that allow major tax deductions for homeownership PIC COLLAGE

B Practice drawing FBDS 10 lb A B O E A AB 0 2 0 5 m A GO B 30 BC 0 1 A B

Dr Scotch s research involves tracking degeneration of myelin in the brains of older adults and its impact on the ability to perform tasks that require fine motor skills Because this is his specific focus which of the meta theories may he subscribe to contextual maturational mechanistic

Q4 Question 1 26 Cont d One of the variables in the Drafting NFL Quarterbacks problem is Quarterback Production Score What type of variable is Quarterback Production Score 1 pt a Quantitative b Qualitative c Cannot tell from the problem statement

The histogram below gives the length of service of members of the Department of Chemistry at a particular university The classes in years of service are 0 4 9 5 9 9 etc and the vertical axis represents the number of faculty What percent of the department faculty have less than 25 years of service Answer 9 8 CO 7 6 12 5 4 3 2 1 8 5 12 18 15 Chemistry Faculty 28 25 38 35 48 Tt

ook int int ences Sydney Retailing buyer and Troy Wholesalers seller enter into the following transactions May 11 Sydney accepts delivery of 37 500 of merchandise it purchases for resale from Troy invoice dated May 11 terms 3 10 n 90 FOB shipping point The goods cost Troy 25 125 Sydney pays 435 cash to Express Shipping for delivery charges on the merchandise May 12 Sydney returns 1 200 of the 37 500 of goods to Troy who receives them the same day and restores them to its inventory The returned goods had cost Troy 804 May 20 Sydney pays Troy for the amount owed Troy receives the cash immediately Both Sydney and Troy use a perpetual inventory system and the gross method 1 Prepare journal entries that Sydney Retailing buyer records for these three transactions 2 Prepare journal entries that Troy Wholesalers seller records for these three transactions Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare journal entries that Sydney Retailing buyer records for these three transactions Check my we

2 19 A research specialist for a large seafood company plans to investigate bacterial growth on oysters and mussels subjected to three different storage temperatures Nine cold storage units are available She plans to use three storage units for each of the three temperatures One package of oysters and one package of mussels will be stored in each of the storage units for 2 weeks At the end of the storage period the packages will be removed and the bacterial count made for two samples from each package The treatment factors of interest are temperature levels 0 5 10 C and sea food levels oysters mussels She will also record the bacterial count for each package prior to plac ing seafood in the cooler Identify each of the following components of the experimental design a Factors b Factor levels c Blocks d Experimental unit e Measurement unit f Replications

The graph of 4x4 8x y 4y4 36x 36y is a lemniscate dy a Find by implicit differentiation dx b Find the slope of the tangent line to the lemniscate at 5 1 a dy dx

3 Homework K Question 17 3 3 20 Use the implicit differentiation of the equation to determine the slope of the graph at the given point y x 41 x 2 y 7 The slope of the graph at the given point is Type an integer or a simplified fraction Points

Suppose an economist wishes to determine the relationship between the age and price of houses A study yields the following data A B O Matched pairs C Inference for regression Two independent samples Worksheet 1 C1 1 2 3 4 5 27 74864 49 35 51 42 C2 87886 48 63 50 72 55 If column 1 is the price in hundreds of thousands of dollars of a sample of five houses from ten years ago and column 2 is the price in hundreds of thousands of dollars of the same homes today which of the following is the appropriate inference method to analyze these data Select one answer 10 points

CAL BIOCHEMISTRY 72 248 254 1976 apid and Sensitive Method for the Quantitation of Microgram Quantities of Protein Utilizing the Principle of Protein Dye Binding MARION M BRADFORD Reproduction Research Laboratories Department of Biochemistry University of Georgia Athens Georgia 30602 Received September 11 1975 accepted January 29 1976 A protein determination method which involves the binding of Coomassie rilliant Blue G 250 to protein is described The binding of the dye to protein auses a shift in the absorption maximum of the dye from 465 to 595 nm and is the increase in absorption at 595 nm which is monitored This assay is ery reproducible and rapid with the dye binding process virtually complete in pproximately 2 min with good color stability for 1 hr There is little or no nterference from cations such as sodium or potassium nor from carbohydrates uch as sucrose A small amount of color is developed in the presence of trongly alkaline buffering agents but the assay may be run accurately by the use of proper buffer controls The only components found to give excessive nterfering color in the assay are relatively large amounts of detergents such as sodium dodecyl sulfate Triton X 100 and commercial glassware detergents Interference by small amounts of detergent may be eliminated by the use of proper controls aboratory practice in protein purification often requires a rapid an sitive method for the quantitation of protein Methods presentl inal primary literature article that describes the Bradford Assay A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein dye binding Then answer the questions below about the article 3 9 pts According to the article Coomassie Brilliant Blue G 250 can be red or blue a What causes the color change from red to blue b Approximately how long does it take for the color to change In the pre lab video instructions stated to incubate Bradford dye protein for 10 minutes According to Figure 3 in the paper how much would the absorbance change if I waited one hour to make my measurement 4 5 pts In the manuscript the author looks at a variety of substances to see if they interfere with the Bradford assay We will be using NaCl in our Buffer this semester Would 50 mM NaCl interfere with the assay at 595 nm Provide evidence for your answer

A researcher wants to find out if U S adults still support the death penalty at a proportion of 0 64 as it was in 2003 This graph indicates the sampling distribution for the proportion of supporters in random samples of 25 adults The standard deviation is approximately 0 10 04 0 5 0 6 0 7 0 8 0 9 What is the approximate test statistic for p 0 84 A O 2 B O 1 C Oo D O1 E O2 Select one 10 points

The random variable X representing the number of items sold in a week has the following probability distribution D 2 0 X F 0 P X x 0 10 1 On average how many items are sold in a week A 6 3 B 3 0 C 2 2 0 20 2 0 40 3 0 15 4 5 0 05 0 05 6 0 05 Select one answer 10 points

In an experiment the probability that event A occurs is 7 occurs is 38 Submit and the probability that event B If A and B are independent events what is the probability that A and B both occur Simplify any fractions

Name that variable A survey of a large college class asked the following questions 1 Are you female or male In the data male 0 female 1 2 Are you right handed or left handed In the data right 0 left 1 3 What is your height in inches 4 How many minutes do you study on a typical weeknight c b d

ture on health in 35 countries with the highest gross domestic product in that year 2 Health expenditure per capita is the sum of public and private TABLE 1 3 Per capita total expenditure on health international dollars Dollars Country Dollars Country 293 Saudi Arabia 1725 1414 South Africa 4191 4885 3126 Spain 4526 3741 Sweden 1454 2398 Switzerland 938 Thailand 4759 646 1061 Turkey 843 5601 United Arab Emirates 4552 207 United Kingdom 4334 6308 United States 4812 1551 Venezuela 215 1587 Argentina Australia Austria Belgium Brazil Canada China Colombia Denmark France Germany India Country Indonesia Iran Italy Japan Korea South Malaysia Mexico Netherlands Nigeria Norway Poland Russia Dollars 1681 1121 2846 4244 6187 658 1053 2233 3311 9146 656 health expenditure in PPP international divided by population Health expenditures include the provision of health services family planning activi ties nutrition activities and emergency aid designated for health but