Probability Questions and Answers

The following data gives the number of failed experiments in the past 12 weeks of the labi 15 9 12 11 7 6 9 10 124 3 6 5 find the percentage rank of 7

You are conduction a scenario analysis for a stock You forecast that the stock price will go up 15 with a 20 chance it will go up 8 with a 50 chance and it will go down 8 otherwise What is the standard deviation of returns from this scenario analysis

Suppose you brought a put option with a strike price of 52 for 3 What would be your payoff if the underlying stock was priced 58 at option expiration 4 3 B 9 C 6 D 3 0

Match each function with its graph 22 1 y sinx 3y sinx M 2 A O 2y csx F cosx 5 pada D AAAAA Choose D B A C Choose Choose

9 65 Determine the location x y of the centroid C of the area 1 5 in 1 5 in 1 5 in 1 5 in Prob 9 65 1 5 in

6 12 Determine the force in each member of the tru and state if the members are in tension or compression A 500 lb 500 lb A 3 3 3 ft Bo 9 ft 3 ft OD Prob 6 12 OE 6 ft 6 ft

Use the data in the Stem Leaf plot to answer the following questions STEM LEAF 05 113 256 3302 4974 52

Directions Given the two sets determine if one set is a subset of the other If yes describe the relationship using proper notation 17 4 months with 31 days B months that start with the letter A

A news service conducted a survey of 1081 adults ages 18 years or older in a certain country August 31 September 2 2015 The respondents were asked Of every tax dollar that goes to the federal government how many cents of each dollar would you say are wasted The four possible responses are that the federal government wastes less than 10 cents between 11 cents and 25 cents between 26 cents and 50 cents or 51 cents or more Of the 1081 individuals surveyed 36 indicated that 51 cents or more is wasted The news service reported that 36 of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent with a margin of error of 4 and a 90 level of confidence Complete parts a through e bellow d List the descriptive statistics Choose the correct answer bellow OA 38 of the individuals surveyed indicated that 51 cents or more is wasted B 36 of all adults 18 years or older in this country believe that 51 cents or more is wasted OC There is a 90 chance surveying 1081 individuals from this country will result in a response that matches how the entire country would respond OD The federal government wastes 51 cerits or more of every dollar they receive

You deposit 300 into a savings account that earns interest annually The function g x 300 1 04 can be used to find the amount of money in the savings account g x after x years What is the range of the function in the context of the problem OR O 0 O 300 Q10 3001

Dwayne wants to redecorate his bedroom and decides to purchase new furniture The following graph could be used to represent the value of the new bedroom furniture fix after x years 1300 1200 1100 1000 900 800 700 600 TY 500 400 300 200 100 20 2 Ol only 4 OI and II only 6 Which of the following statements is are true based on the graph and the context of the problem Ol and Ill only 8 10 12 14 1 The function is positive on its entire domain II The domain is x 20 to represent the number of years after the bedroom furniture was purchased III The x intercept 0 1100 represents the initial cost of the bedroom furniture 16 18

Which of the following expressions is equivalent to 24x 5 O O 10 5 16 32 0

What is the NPV of the following project if cost of capital is 11 Round to the nearest dollar Investment today 136 000 Cash inflow in year 1 63 000 Cash inflow in year 2 74 000 Cash inflow in year 3 63 000 Hint Inflows are mixed cash flows so you need to compute PV inflows as the sum of discounted values of those individuals cash flows

9 This section contains EIGHT questions Each question has FOUR options A B C and D ONE OR MORE THAN ONE of these four option s is are correct For each question darken the bubble s corresponding to all the correct option s in the ORS Marking scheme 4 If only the bubble s corresponding to all the correct option s is are darkened 0 If none of the bubbles is darkened 2 In all other cases 50 Let f x 192x 2 sin rx m and Mare A m 13 M 24 C m 11 M 0 for all x ER with 51 If a 3 sin 2 0 If m 0 If m f x dx M then the possible values of 1 2 Let S be the set of all non zero real numbers a such that the quadratic equation ax x a 0 has two distinct real roots x and x2 satisfying the inequality x x 1 Which of the following intervals is are a subset s of S A 12 3 0 0 5 and B 3 cos 1 B m M 2 D m 1 M 12 B 50 52 D where the inverse trigonometric functions take only the principal

Let m and n be two positive integers greater than 1 If ecos a lim a 0 a e then the value of m n is e

Smithson Cutting is opening a new line of scissors for supermarket distribution It estimates its fixed cost to be 500 00 and its variable cost to be 0 55 per unit Selling price is expected to average 0 75 per unit a For Smithson Cutting the break even point in units units enter your response as a whole number b For Smithson Cutting the break even point in dollars round your response to the nearest whole number

13 Kevin selects one card from a deck of 52 cards If it is an ace he wins 5 If it is a club he wins only 1 However if it is the ace of clubs then he wins an extra 10 What is his mathematical expectation Suppose it costs him 1 to play the game What could he expect to win or lose per game

Consider a company with trailing EPS of 4 and forecasted next year EPS of 5 If comparable companies are trading at a forward PE multiple of 20 what s the estimated value of this company s shares using relative valuation

Consider a stock with a share price of 92 trailing earnings per share of 4 and forecasted earnings per share for the following year of 5 What is this stock s trailing PE ratio Round to one decimal place

For the figure shown below determine the moment of the force F about an axis extending between points D and C Express the result as a cartesian vector and show its unit Use F 200 KN x 2 m D 2 m 2 m z 2 m 3 m A C E B F Y

An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips The mean tip percentages and standard deviations are given in the accompanying table along with the sample sizes Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b State the conclusion for the test No candy H Two candies H2 40 21 15 2 34 n 40 X S 18 33 1 47 A Reject the null hypothesis There is sufficient evidence to support the claim that giving candy does result in greater tips OB Fail to reject the null hypothesis There is sufficient evidence to support the claim that giving candy does result in greater tips b Construct the confidence interval suitable for testing the claim in part a H H Round to two decimal places as needed n 4 OC Reject the null hypothesis There is not sufficient evidence to support the claim that giving candy does result in greater tips OD Fail to reject the null hypothesis There is not sufficient evidence to support the claim that giving candy does result in greater tips

Claim More than 3 5 of homes have only a landline telephone and no wireless phone Sample data A survey by the National Center for Health Statistics showed that among 15 647 homes 5 83 had landline phones without wireless phones Complete parts a and b a Express the original claim in symbolic form Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone H ger or a decimal Do not round

Samples results are listed below Construct a 90 confidence interval estimate of the mean What is the practical use of the confidence interval 1 1 2 4 3 3 3 4 4 2 C What is the confidence interval for the population mean 2 3 4 Round to one decimal place as needed What is the practical use of the confidence interval Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The confidence interval can be used to estimate that 90 of all people have DNA bases between and Round to one decimal place as needed OB The given numbers are just substitutes for the four DNA base names so the numbers do not measure or count anything and they are at the nominal level of measurement The confidence interval has no practical use OC The confidence interval can be used to estimate that with 90 confidence the interval from to actually contains the true mean DNA base of all people Round to one decimal place as needed

A sample of birth weights of 36 girls was taken Below are the results in g 2681 8 3605 5 3955 6 2591 7 2638 6 3881 9 3149 9 2850 4 2792 1 3757 3 3339 2768 4 2812 8 3655 6 3433 9 3117 5 3341 8 3921 4 4002 4 3756 5 3424 5 3818 3 3726 5 3289 3456 5 2910 3683 5 3560 9 3388 5 3082 1 2828 3181 8 3115 6 3344 4 3064 2 3836 Note The average and the standard deviation of the data are respectively 3326 8 g and 419 7 g Use a 1 significance level to test the claim that the standard deviation of birthweights of girls is different from the standard deviation of birthweights of boys which is 480 g Procedure Select an answer O Assumptions select everything that applies O Population standard deviation is unknown The number of positive and negative responses are both greater than 10 O Population standard deviation is known Sample size is greater than 30 O Simple random sample O Normal population

F4 37 Determine the resultant force and specify where it acts on the beam measured from A 6 kN m 1 5 m 9 kN m 3 m B Prob F4 37 3 kN m 1 5 m F4 40 Determine the resultant force and specify where it acts on the beam measured from A

University of Florida football programs are printed 1 week prior to each home game Attendance averages 90 000 screaming and loyal Gators fans of whom two thirds usually buy the program following a normal distribution for 5 each Unsold programs are sent to a recycling center that pays only 10 cents per program The standard deviation is 5 000 programs and the cost to print each program is 1 Refer to the standard normal table for z values a What is the cost of underestimating demand for each program C round your response to two decimal places

4 What type of reaction is present in a fixed support Vertical horizontal and moment O Vertical and Horizontal O Moment only O None of the options All options are correct except none of the options O Vertical and Moment O Vertical only D Question 5 5 For this beam how many pin support 2 5 pts

Dave Fletcher was able to determine the activity times for constructing his laser scanning machine Fletcher would like to determine ES EF LS LF and slack for each activity The total project completion time and the critical path should also be determined Here are the activity times Q Activity Time weeks Immediate Predecessor s Activity Time weeks Immediate Predecessor s A B C D 7 6 4 3 A A Dave s earliest start ES and earliest finish EF are Activity ES EFG H EF 7 4 5 11 6 B B C E D F

1 Internal forces are not shown on a free body diagram because the internal forces are Choose the most appropriate answer Equal and opposite and they do not affect the calculations Negligibly small O Not important O Equal to zero

Lake Martin and Lake Fields are two large local lakes inhabited by white sturgeon A while back there was an environmental disaster at Lake Martin Debra is an ecologist who wants to see if the mean weight in kg of adult white sturgeon now living in Lake Martin is less than the mean weight in kg of adult white sturgeon now living in Lake Fields The ecologist catches a random sample of 10 adult white sturgeon at Lake Martin and a random sample of 12 adult white sturgeon at Lake Fields These samples are chosen independently Each fish has its weight in kg recorded These data are shown in the table Weights in kg Lake Martin sturgeon 73 5 78 2 80 6 86 4 72 4 71 1 85 1 81 8 79 0 79 7 Lake Fields sturgeon Send data to calculator 124 0 101 9 81 8 66 6 62 7 79 4 115 5 113 3 94 5 75 8 94 0 105 1 Assume that the two populations of weights are approximately normally distributed Can the ecologist conclude at the 0 05 level of significance that the population mean of the weights of adult white sturgeon now living in Lake Martin is less than the population mean of the weights of adult white sturgeon now living in Lake Fields Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis H and the alternate hypothesis H HO H 0 b Determine the type of test statistic to use Degrees of freedom 0 c Find the value of the test statistic Round to three or more decimal places 0 d Find the critical value Round to three or more decimal places e At the 0 05 level of significance can the ecologist conclude that the mean weight of adult white sturgeon now living in Lake Martin is less than the H x a S P Q 0 48 O 0 ORO 050 0 0 0 0 Est

The Senators have won 75 of the games played against the Canadiens over the past few seasons What is the probability that the Canadiens will win exactly 4 of the 8 games they play against the Senators this season O 0 087 O 0 25 O 0 011 O 0 069

In a large clinical trial 400 753 children were randomly assigned to two groups The treatment group consisted of 201 136 children given a vaccine for a certain disease and 26 of those children developed the disease The other 199 617 children were given a placebo and 91 of those children developed the disease Consider the vaccine treatment group to be the first sample Identify the values of n P 9 n P2 92 p and q 1 n

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress Among 277 vinyl gloves 65 leaked viruses Among 277 latex gloves 13 leaked viruses Using the accompanying display of the technology results and using a 0 05 significance level test the claim that vinyl gloves have a greater virus leak rate than latex gloves Let vinyl gloves be population 1 Click the icon to view the technology results What are the null and alternative hypotheses OA Ho P1 P2 H P P2 O D Ho P1 P2 H P P2 OB Ho P P2 H P P2 O E Ho P H P P2 P2 OC Ho P1 P2 H P P2 OF Ho P1 H P P2 P2

Since an instant replay system for tennis was introduced at a major tournament men challenged 1395 referee calls with the result that 420 of the calls were overturned Women challenged 771 referee calls and 216 of the calls were overturned Use a 0 05 significance level to test the claim that men and women have equal success in challenging calls Complete parts a through c below a Test the claim using a hypothesis test Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls What are the null and alternative hypotheses for the hypothesis test OA Ho P1 P2 H P P2 OD Ho P SP2 H P P2 OB Ho P1 P2 H P P2 O E Ho P P2 H P P2 OC Ho P P2 H P P2 OF Ho P1 H P P2 P2

2x y 2xy 0 is y 6 0 0 0 0 x 1 ft y t dt x 0 is 0 2 y 1 ger 4 cx ex slope of tangent at any of the abscissa to the and yil 19 citr ercepts of a tangent at double of the x and y e of whose tangent at hich passes through 1 off between origin and tangent abscissa of point of contact is kx3 1 y C 3 et 3 kx 3 y 2 15 A curve y f x passes through point P 1 1 The normal to curve at point P is a y 1 x 1 0 If slope of tangent at any point on curve is proportional to ordinate at that point then equation of curve is 1 y eax 1 2 y eax 1 3 y e x a 4 y e x 1 X C dy dx The foci of the curve which satisfies the equation 1 y dx xy dy 0 and passes through the point 1 0 are palang 1 2 0 2 0 2 3 2 0 4 0 2 2 The general solution of the equation kx3 2 SECTION B Objective Type Questions One or more than one option s is are correct dy dx 2 y y In y x is CX kx cx 3 2 4 y x y 1 y xet cx V y xet cx 3 y xe ex 4 y xecx The equation of the curve passing through 3 4 anc satisfying the differential equation dy x 0 can be dx

1 AB 1 3 A B 0 13 If x x 3 2x1 6 x 1 x 3 then 1 A 3 3 2 sent the value of g 3 A 3 OVG 14 Let a function f R 0 R satisfy the equation f x y f x 2xf y y and 1 41 5 57 2 e 5 g 0 where g x ff e5x cos4x dx then 41 5 5T 2 1 4 C D 0 A x2 3 Btan 1 x1 6 c 7 2 B 12 T 4 B can be 1 6 5 2 5 e 41 4 17112016 252 5 5 LO 5T 2 2 E 2 1 51 tranq 200

A pharmaceutical company receives large shipments of aspirin tablets The acceptance sampling plan is to randomly select and test 41 tablets then accept the whole batch if there is only one or none that doesn t meet the required specifications If one shipment of 7000 aspirin tablets actually has a 5 rate of defects what is the probability that this whole shipment will be accepted Will almost all such shipments be accepted or will many be rejected The probability that this whole shipment will be accepted is Round to four decimal places as needed

Consider company with revenues of 20 million this year The company is projected to grow its revenue 10 over the next year What is its projected free cash flow next year if it is forecasted to have the following characteristics Operating margin 60 Tax rate 15 Reinvestment rate 45 Assume that the company has no non operating income so that EBIT Operating income Answer in millions showing one decimal place e g 45 318 910 45 3 Hint Step 1 Calculate next year s revenue projecting by applying the projected growth rate to this year s revenues Step 2 Calculate next year s operating income using next year s revenues and operating margin Step 3 Take the operating income as the company s EBIT and plug that in the FCFF formula

1 Build a rule to show the total number of 1 foot by 1 foot sandstone tiles needed to tile a room of length x plus the 6 square feet for the front porch 2 Use a graphing calculator to graph both y x2 and the new function rule 3 How does adding six 1 by 1 tiles change the graph of the original function rule y x the parabola 4 How will the graph of the original function rule y x change if Carly and Rodrigo need only four 1 foot sandstone tiles for the porch 5 How will the graph of the original function rule y x change if Carly and Rodrigo need ten 1 foot sandstone tiles for the porch

Question 3 3 If F1 1 N x1 1 m F2 2 Newton and x2 2 meters what is the location of FR i e the distance x X2 O 1 67m O2m X1 O 1 33m O 1m F F15 F 2 5 pts X FR

4 Find Fr 100 N m O 100 N O 12 N O 1200 N 600 N 12 m

2 1 A coin is tossed twice and the four possible outcomes are assumed to be equally likely If A is the event both head and tail have appeared and B the event at most one de tail is observed then the value of P B A is 1 1 3 1 2 2 20 4 1 4 6

1 Value x of X 0 2 4 2 5 6 3 X 0 13 Fill in the P X x values to give a legitimate probability distribution for the discrete random variable X whose possible values are 0 2 4 5 and 6 P X x 0 23 0 17 0 4 F 5 6 7 8 9 10 11 12 13

6 8 6 10 x 12 13 14 16 A TV executive is interested in the popularity of a particular streaming TV show She has been told that a whopping 68 of American households would be interested in tuning in to a new network version of the show If this is correct what is the probability that all 6 of the households in her city being monitored the TV industry would tune in to the new show Assume that the 6 households constitute a random sample of American households Round your response to at least three decimal places If necessary consult a list of formulas 0 18

An annual coupon bond has a face value of 1 000 and a coupon rate of 6 0 Time to maturity is 16 years and the current yield to maturity is 7 5 What percentage of this bond s value is due to its face value Answer in percent rounded to one decimal place e g 54 67 54 7 Hint PV of the face value of a bond is given by the second term in the coupon bond value formula Find the PV of the face value and divided it by the total value of the coupon bond

a Determine the magnitude and direction angles of the resultant force acting on A Use Fab 80 lb Fac 120 lb PA 2ft B 5 I w P 61 FAC C 4

Determine the magnitude of resultant force of the addition of Fa and Fb Fr Fa Fb the coordina direction angles and check whether it satisfies the direction cosines additions condition 120 60 45 F 200N 35 25 Fb 400N

2 5 6 7 8 S 10 From experience an airline knows that only 85 of the passengers booked for a certain flight actually show up If 8 passengers are randomly selected find the probability that at most 6 of them show up Carry your intermediate computations to at least four decimal places and round your answer to two decimal places If necessary consult a list of formulas 0

Suppose that the age of students at George Washington Elementary school is uniformly distributed between 5 and 11 years old 49 randomly selected children from the school are asked their age Round all answers to 4 decimal places where possible a What is the distribution of X X U Suppose that 49 children from the school are surveyed Then the sampling distribution is b What is the distribution of N c What is the probability that the average of 49 children will be between 8 and 8 5 years old

Question 4 A store manager gathers some demographic information from the store s customers The following chart summarizes the age related information they collected Age Number of Customers 20 20 29 30 39 40 49 50 59 60 88 86 57 68 64 67 One customer is chosen at random for a prize giveaway Round answers to 4 decimal places a What is the probability that the customer is at least 20 but no older than 39 b What is the probability that the customer is either older than 60 or younger than 40 c What is the probability that the customer is at least 60