Statistics Questions and Answers

Steel rods are manufactured with a mean length of 27 centimeter cm Because of variability in the manufacturing process the lengths of the rods are approximately normally distributed with a standard deviation of 0 06 cm Click the icon to view a table of areas under the normal curve 0 0196 Round to four decimal places as needed c Using the results of part b if 5000 rods are manufactured in a day how many should the plant manager expect to discard 98 Use the answer from part b to find this answer Round to the nearest integer as needed d If an order comes in for 10 000 steel rods how many rods should the plant manager expect to manufacture if the order states that all rods must be between 26 9 cm and 27 1 cm Round up to the nearest integer

the value of Za 0 279 Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 www The value of Z0 279 is Round to two decimal places as needed

Find the Z scores that separate the middle 79 of the distribution from the area in the tails of the standard norma distribution Click the icon to view a table of areas under the normal curve The Z scores are Use a comma to separate answers as needed Round to two decimal places as needed

The number of chocolate chips in an 18 ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips a What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips b What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips c What proportion of bags contains more than 1175 chocolate chips d What is the percentile rank of a bag that contains 1000 chocolate chips Click the icon to view a table of areas under the normal curve a The probability that a randomly selected bag contains between 1100 and 1400 chocolate chips is Round to four decimal places as needed

The lengths of a particular animal s pregnancies are approximately normally distributed with mean 256 days and standard deviation 8 days a What proportion of pregnancies lasts more than 266 days b What proportion of pregnancies lasts between 252 and 258 days c What is the probability that a randomly selected pregnancy lasts no more than 246 days d A very preterm baby is one whose gestation period is less than 236 days Are very preterm babies unusual Click the icon to view a table of areas under the normal curve a The proportion of pregnancies that last more than 266 days is Round to four decimal places as needed

Find the value of Za 20 21 Click the icon to view a table of areas under the normal curve Z0 21 Round to two decimal places as needed

Find the general solution of the given second order differential equation 7y y 0 C cos 7 x C sin 7 x COS y x XX

Click the icon to view a table of areas under the normal curve is the Z score such that the area under the curve to the left is 0 52 Round to two decimal places as needed Tables of Areas under the Normal Curve 8 7 02420 0 2399 02358 02327 0 2296 1 4 45 0 4 1 AI 4 8 8 0 PO 12 0 2743 02709 02676 02643 0311 02578 0 03085 03050 0 3015 029 02913 0 8 3 RA 0 3446 03409 0 3372 0 1156 03364 0 3821 0 3783 03745 0 3707 0369 03632 B 042307 04168 04129 0 4750 04252 04011 0 3 0 4602 0 4962 04522 044503 0 4443 04404 04 OSE GAND 1493 0 4500 01 45 40 11 4501 04 0 5000 0 5040 0 500 0 3120 05180 03399 0 5 0 5398 0 543 0 5478 0 5517 0 5557 5590 8 58 LIEVO ALIVO WILD BASSA BASRI 8 3 05743 0 3833 0 5871 0 50 0 5948 0 5987 063 0 6293 GAX31 0638 064 816664 0630 06736 067 SSTVO SCWD WCZO OOKE D D

24 J 1 2 3 4 A fx B C Bumpkins currently finances with 30 0 debt i e changing the capital structure to wa 60 0 by issu repurchase and retire co mon shares so the perce structure 1 Wd Given the data shown below by the firm s cost of equity Calculate the current cost of equity in B21 current unlevered beta in B22 the new beta in B23 the ne of equity in B25

Suppose that the efficacy of a certain drug is 0 59 Consider the sampling distribution sample size n 127 for the proportion of patients cured by this drug a What is the mean of this distribution 0 59 O 0 59 b What is the standard error of this distribution Round the answer to three decimal places

2 Cards You draw a card at random from a standard deck of 52 cards If you draw an Ace and a Heart you win 27 If you draw a King or a Diamond you win 6 Otherwise you lose 5 the cost to play

Determine if each game is a fair game If the game is not fair find the fair price of the game 1 Dice You roll a red 4 sided die and a blue 4 sided die If the blue die s roll is higher you gain 6 points If the red die s roll is higher you lose 2 points the cost to play If the two dice rolls tie you lose 1 point

Question 5 5 3 11 points Points 0 of 1 the final amount in the following retirement account in which the rate of return on the account and the time 000 per quarter invested at 4 5 compounded quarterly for 12 years then 1900 per quarter invest mpounded quartery for 17 years d the final amount in the account Do not round until the final answer Then found to the nearest dollar as needed

The city of Raleigh has 6 100 registered voters There are two candidates for city council in an upcoming election Brown and Feliz The day before the election a telephone poll of 300 randomly selected registered voters was conducted 133 said they d vote for Brown 157 said they d vote for Feliz and 10 were undecided Give the sample statistic for the proportion of voters surveyed who said they d vote for Brown Round your answer to four decimal places This sample statistic suggests that we might expect voters to vote for Brown of the 6 100 registered

Animal Mass kg Cow Human a Sheep Hen Rat Dove 400 70 45 2 0 3 0 16 If the metabolism equation for the given model is y ame then determine the best fit coefficient a power B and using the given data Round the final answers to four decimal places The values of a B and are as follows B 2 1 0 98 Metabolism watts 270 82 50 4 8 1 45 0 97 Show Transcribed Text the metabolism equation for th iven model is y am then etermine the best fit coefficient power B and 2 using the giver ata Round the final answers to our decimal places

Kthrough d below Bicy is used when system reliability is improved through redundant or backup components Assume that a student s alarm clock has a 19 1 daily failure rate Complete pa a What is the probability that the student s alarm clock will not work on the morning of an important final exam Round to three decimal places as needed b If the student has two such alarm clocks what is the probability that they both fall on the morning of an important final exam Round to five decimal places as needed c What is the probability of not being awakened if the student uses three independent alarm clocks Round to five decimal places as needed d Do the second and third alarm clocks result in greatly improved reliability OA No because total malfunction would still not be unlikely OB Yes because total malfunction would not be impossible but it would be unlikely OC No because the malfunction of both is equally or more likely than the malfunction of one OD Yes because you can always be certain that at least one alarm clock will work

You are making your schedule for next semester You have 13 choices for your math class 12 choices for your English class 9 choices for your communications class and 6 choices for your elective How many different schedules are possible There are different schedules possible

A group of 5 students is to be chosen from a 27 member class to represent the class on the student counci How many ways can this be done NOTE Order of the selection is not important Answer ways

A true false test contains 8 questions In how many different ways can this test be completed Assume we don t care about our scores This test can be completed in Quertion Hol DVA 521 different ways

QUESTION 21 The following table shows results from a Poisson GLM generalized linear regression mo in response to three predictor variables Food treatment Parent sex and arrival time and Link the correct statements below based on this information Intercept FoodTreatmentSatiated Arrival Time SexParentMale Food TreatmentSatiated Sex ParentMale Food TreatmentSatiated Arrival Time Estimate 5 169 0 654 0 221 0 121 0 129 0 001 Std Error 0 292 0 011 0 018 0 021 0 070 0 019 p va 0 00 0 0 0 03 0 0 0 06 0 97

QUESTION 9 Disaster The statistical software is broken However you to produce the test score round the score to one decin

QUESTION 14 Based on plotting tail length vs toxin content you decide to use a simple linear regression to test the relationship You already know that t normality Resida s mandardized residus 9 8 8 9 8 50 01 100 Residuals vs Fitted 150 200 Fided values Im Toun ng Tail mm Normal Q Q 250 240 219 300 260

A pizza parlor offers a choice of 12 different toppings How many 5 topping pizzas are possible no double orders of toppings are allowed In this situation does the order of the toppings matter Input yes or no There are possible 5 topping pizzas

How many different 5 card hands can be dealt from a deck of 52 cards The order of the cards does not matter in this case Your answer is

In a lottery daily game a player picks three numbers from 0 to 9 without repetition How many different choices does the player have a If order matters b If order does not matter

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity Wind speeds must average more than 12 miles per hour mph for a site to be acceptable Recently the organization conducted wind speed tests at a particular site Based on a sample of n 110 wind speed recordings taken at random intervals the wind speed at the site averaged X 11 2 mph with a standard deviation of s 3 5 mph To determine whether the site meets the organization s requirements consider the test Ho 12 vs HA 12 where is the true mean wind speed at the site and a 0 05 Fill in the blanks A Type I error in the context of this problem is to conclude that the true mean wind speed at the site 12 mph when it actually 12 mph is at most exceeds exceeds is at most exceeds exceeds equals exceeds equals equals

The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year and the color of their cars Speeding Ticket Red Car Not Red Car Total b Has a speeding ticket 94 183 277 Find the probability that a randomly chosen person a Has a red car No Speeding Ticket 136 135 271 c Has a speeding ticket given they have a red car d Has a red car given they have a speeding ticket e Has a red car and got a speeding ticket Fue Total 230 318 548 f Has a red car or got a speeding ticket Write your answers in decimal form rounded to the nearest thousandth

An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 5 days and an alternative hypothesis that the average time for processing a claim is greater than 5 days After completing the statistical test it is concluded that the average time exceeds 5 days However it is eventually learned that the mean process time is really 5 days What type of error occurred in the statistical test O Type Il error Type I error O alpha error O No error occurred in the statistical sense beta error

QUESTION 15 The model output for the simple linear regre Model Toxin ng Tail mm Residuals Min 1Q Median 3Q Max 61 958 8 286 3 026 16 246 28 774

QUESTION 13 Following your adventures on the monkey islands you are asked to collaborate on a new project Some researc species of lizard Bigger lizards have more brightly coloured tails and the scientists suspect that the bright colou dropped by 27 random female lizards You measure their length 15 300 mm and toxin content 22 330 ng and Toxin ng 300 250 200 150 100 50 O 50 O O O O 100 150 0 00 200 250 O O 8 30

Suppose we collect data on snacks found at a certain store The histogram shown below shows a summary of the calories found Frequency 42 10 8 N 220 230 240 250 260 270 280 290 Calories What is the frequency of snacks that had at least 270 calories Which will be true of the histogram above Mean will be higher than the median Mean will be lower than the median Mean and median will be about the same

During the summer there is an average of 5 fireflies with a standard deviation of o 1 1 fireflies that visit your porch The number of fireflies is bell shaped Use the Empirical Rule to find the percentage of days that the following number of fireflies visit you Use exact answers a between 1 7 and 7 2 fireflies b at least 7 2 fireflies To the best of your ability explain how you got your answer to the this problem One way to do so is to describe the picture you drew to figure out the answer

A study is done to see how long it takes songwriters to write a song A survey of 32 songwriters was conducted and each one was asked How many days on average does it take you to finish writing a song The answers were collected and recorded in the table below 5 7 8 8 14 15 18 18 22 23 1 9 15 19 Number of Days 0 3 4 7 8 11 12 15 16 19 3 10 16 20 23 20 5 12 16 20 14 16 21 Find the frequencies for the classes below and put them in the table Leave answers in reduced fractions where appropriate Do not use decimals 6 Frequency 14 17 22 14 17 22 Relative Frequency

A boutique wants to study the customers who purchase items through their website The manager selects 54 random online orders and records the amount spent The average amount spent was 29 13 Match the following terms with the correct aspects of the study All customers who purchase items through the boutique s website The true average amount spent by all customers on the boutique s website The 54 random online orders in the study The answer Dollar amount spent on the website The list of 54 dollar amounts recorded from the selected online orders The average amount spent on the 54 selected orders a Population b Sample c Parameter d Variable e Statistic f Data

A researcher surveyed adults and recorded the number of miles they drove their car in one year The results are in the boxplot below and the annual number of miles is measured in 1000 s 6 8 8 5 12 4 16 5 10 15 20 Thousands of Miles Driven Annually What is the minimum of the number of miles found thousand miles 23 25 Twenty five percent of the number of miles fall below what value thousand miles Twenty five percent of the number of miles fall above what value

According to the Pew Research Centers Millenials are the most likely generation to use public libraries published June 21 2017 Suppose you have a sample of 8 millenials and ask How many times have you visited a public library in the past month The results are shown below 3 6 7 7 10 11 12 12 Find the 5 number summary for the data Min Q1 Q2 Q3 Max Find the IQR for the data IOR

Lacy draws a 6 from a standard deck of 52 cards She replaces the first card and then draws a second card and gets a 4 Are these events independent or not Explain

Match the terms to the correct symbols N gives the Population Mean Sample Mean O Population Size Sample Size Population Standard Deviation Sample Standard Deviation gives the Population Mean Sample Mean Population Size Sample Size Population Standard Deviation Sample Standard Deviation s gives the Population Mean Sample Mean Population Size Sample Size Population Standard Deviation Sample Standard Deviation

try the sampling technique a LA County wants to survey the morale of residents in the county during the period of COVID quarantine To do so they survey 100 random people in each city within the county O Cluster Sampling Systematic Sampling Convenience Sampling Stratified Sampling Simple Random Sampling the scenarios below b A Frontier representative wants to know how satisfied people in a neighborhood are with their internet service To find out he tries to survey people at every 3rd house in the neighborhood O Cluster Sampling Systematic Sampling Convenience Sampling Stratified Sampling

A plane rises from take off and flies at an angle of 6 with the horizontal runway When it has gained 500 feet find the distance to the nearest foot the plane has flown The plane has flown approximately c B 500 ft feet Round to the nearest foot

Use a calculator to find the value of the acute angle 0 in radians tan 0 0 3244 0 radians Round to four decimal places as needed

Perine Company has 1 640 pounds of raw materials in its December 31 2019 ending inventory Required production for January and February of 2020 are 4 100 and 5 600 units respectively 2 pounds of raw materials are needed for each unit and the estimated cost per pound is 6 Management desires an ending inventory equal to 20 of next month s materials requirements Prepare the direct materials budget for January PERINE COMPANY Direct Materials Budget

B 24 Simple random samples of 40 CA high school seniors and 35 NJ high school seniors are conducted The number of sports clubs that a CA senior participated in during his her junior year is uniformly distributed with a mean of 15 9 and a standard deviation of 6 3 The number of sports clubs that a NJ senior participated in during his her junior year is skewed to the left with a mean of 14 8 and a standard deviation of 4 1 What is the probability that the sample mean for CA exceeds the sample mean for NJ A Check the R N I conditions Write the probability statement in terms of D where D Mean for CA Mean for NJ Convert to Z scores and write the probability statement in terms of Z Draw the related picture of the Normal Distribution using the Z scores Find the answer and in

Q3 A simple random sample of 40 CA high school seniors is conducted that a senior participated in during his her junior year is Normally distributed with a mat standard deviation of 5 8 A senior is randomly selected Let X number of clubs sports that a se participated in during his her junior year What is the probability that X is between 10 and 147 A Check the R N I conditions R randomly selected Find the answer on 13 B Write the probability statement in terms of X Convert to Z scores and write the probability statement in terms of Z Draw the related picture of the Normal Distribution using the Z score P 105 YS 14 P 10 3 2 14 13 3 8 U P S1724 2 1724

Q1 The success rate of the Math Fun middle school enrichment program is estimated to be 85 Success is defined as an increase in a child s mathematics achievement score of at least 80 from the beginning to the end of the program A simple random sample of 100 middle school children is selected from a population of 100 203 middle school children What is the probability that the success rate for the sample is between 0 83 and 0 88 A Check the R N I conditions Random normalr Independent B Write the probability statement in terms of p hat Convert to Z scores and write the probability statement in terms of Z Draw the related picture of the Normal Distribution using the Z scores P 83 X 88 83 185 0 0357 It says it is a Sample It is a simple random normally distributed to students It s independent by NEION 100 10 1 00 0 02 0 0357 x EXC X 88 85 0 0357 x P 1 P P 0 5602x 0 8403 C Find the answer and interpret the answer in context 83 85 Carm 100 0 03 0 0357 SD 0 035707 0 035 FOOT C 85 1 85 85 1 N 88 85 D 67

A dartboard has 8 equally sized slices numbered from 1 to 8 Some are grey and some are white The slices numbered 5 6 and 7 are grey The slices numbered 1 2 3 4 and 8 are white A dart is tossed and lands on a slice at random Let X be the event that the dart lands on a grey slice and let P X be the probability of X Let not X be the event that the dart lands on a slice that is not grey and let P not X be the probability of not X a For each event in the table check the outcome s that are contained in the event Then in the las probability of the event Event X not X b Subtract Outcomes P X P not X e 1 2 3 4 5 6 7 8 D 1 P X c Select the answer that makes the sentence true 1 P X is the same as Probability P X P not X

A spinner with 12 equally sized slices is shown stops on a slice at random What is the probab Write your answer as a fraction or a whole num

A certain disease has an incidence rate of 0 7 If the false negative rate is 8 and the false positive rate is 5 compute the probability that a person who tests positive actually has the disease Give your answer accurate to at least 3 decimal places Question Help 161

during a year the average operating cost is 12 3 cents per kilometer If a truck is driven only 118 000 kilometers during a year the average operating cost increases to 15 5 cents per kilometer Required 1 Using the high low method estimate the variable operating cost per kilometer and the annual fixed operating cost associated the fleet of trucks 2 Express the variable and fixed costs in the form Y a bx 3 If a truck were driven 147 000 kilometers during a year what total operating cost would you expect to be incurred Complete this question by entering your answers in the tabs below Required 1 Required 2 Required 3 Using the high low method estimate the variable operating cost per kilometer and the annual fixed operating cost associated with the fleet of trucks Do not round your intermediate calculations Round the Variable cost per kilometer to 3 decimal places Variable cost Fived 0 059 per kilometer

Find the test statistics to test the hypothesis that the means of two populations are equal Two samples are randomly selected and come from populations that are normal The sample statistics are given below Sample Size 25 Sample Mean 25 Sample SD 1 5 3 913 O 3 287 O 1 986 Population 1 Population 2 30 23 1 9 03893