Statistics Questions

Fill in the blanks to complete the sentences below a As the number of samples increases the proportion of 95 confidence intervals that include the population proportion approaches b If a 95 confidence interval results in a sample proportion that does not include the population proportion then the sample proportion is more than standard errors from the population proportion This is a reading assessment question Be certain of your answer because you only get one attempt on this question a As the number of samples increases the proportion of 95 confidence intervals that include the population proportion approaches 0 99 1 0 05

One environmental group did a study of recycling habits in a California community It found that 72 of the aluminum cans sold in the area were recycled Use the normal approximation Round your answers to four decimal places a If 392 cans are sold today what is the probability that 300 or more will be recycled b of the 392 cans sold what is the probability that between 260 and 300 will be recycled

A new muscle relaxant is available Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed with mean 38 minutes and standard deviation o 5 minutes a The drug is administered to one patient selected at random What is the probability that the time it takes to go into effect is 35 minutes or less Round your answer to four decimal places b The drug is administered to a random sample of 10 patients What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less Round your answer to four decimal places c Comment on the differences of the results in parts a and b The probability in part b is the same as the probability in part a because the mean smaller for the x distribution

From public records Individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study Two random samples from this group were studied In the first sample of 31 Individuals the respondents were asked in a face to face interview if they had been charged with drunken driving in the last 12 months Of these 31 people interviewed face to face 14 answered the question accurately The second random sample consisted of 48 people who had been charged with drunken driving During a telephone interview 23 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months Assume the samples are representative of all people recently charged with drunken driving USE SALT a Let p represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face to face interview asking if they have been charged with drunken driving during the past 12 months Let p represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview Find a 90 confidence interval for p P Round your answers to three decimal places lower limit upper limit

Three circle red on white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at an archaeological site At one excavation a sample of 177 potsherds indicated that 80 were of the three circle red on white pattern AUSE SALT a Find a point estimate p for the proportion of all ceramic potsherds at this site that are of the three circle red on white pattern Round your answer to four decimal places b Compute a 95 confidence interval for the population proportion p of all ceramic potsherds with this distinctive pattern found at the site Round your answers to three decimal places lower limit upper limit

A study considered the question Are you a registered voter Accuracy of response was confirmed by a check of city voting records Two methods of survey were used a face to face interview and a telephone interview A random sample of 92 people were asked the voter registration question face to face Of those sampled seventy eight respondents gave accurate answers as verified by city records Another random sample of 84 people were asked the same question during a telephone interview Of those sampled seventy three respondents gave accurate answers Assume the samples are representative of the general population USE SALT a Let p be the population proportion of all people who answer the voter registration question accurately during a face to face interview Let p be the population proportion of all people who answer the question accurately during a telephone interview Find a 95 confidence interval for P P2 Round your answers to three decimal places lower limit upper limit b Does the interval contain numbers that are all positive all negative mixed Comment on the meaning of the confidence interval in the context of this problem At the 95 level do difference in

A random sample of 19 wolf litters in Ontario Canada gave an average of x 4 7 wolf pups per litter with estimated sample standard deviation s 1 1 Another random sample of 7 wolf litters in Finland gave an averag of x 2 8 wolf pups per litter with sample standard deviation s 1 3 LAUSE SALT a Find an 85 confidence interval for the difference in population mean litter size between Ontario and Finland Round your answers to one decimal place lower limit

Three experiments Investigating the relation between need for cognitive closure and persuasion were performed Part of the study involved administering a need for closure scale to a group of students enrolled in an Introductory psychology course The need for closure scale has scores ranging from 101 to 201 For the 74 students in the highest quartile of the distribution the mean score was x 177 70 Assume a population standard deviation of a 8 29 These students were all classified as high on their need for closure Assume that the 74 students represent a random sample of all students who are classified as high on their need for closure How large a sample is needed if we wish to be 99 confident that the sample mean score is within 2 2 points of the population mean score for students who are high on the need for closure Round your answer up to the nearest whole number USE SALT students

Plot these points OF 6 8 7 6 54 3 2 2 21367X 8 9 56781 9 2 3 4 5 6 7 8 9 10 4

computer program or a standard chapter from a textbook to teach students to use fractions The school did a pilot study of the achievement levels where students were randomly assigned to one of the conditions The school obtained the following results Computer Mediated Approach 97 89 95 79 93 Textbook Approach 58 90 75 83 47 Question 1 Use summary calculations of the mean standard deviation and range for each condition to describe the characteristics of the two samples What can you tell the school district about these two samples based on your descriptive analyses Explain what the mean standard deviation and the range mean in simple terms and in complete sentences Question 2 The school wants you to tell them if there is a difference in achievement levels between the computerized and standard textbook groups Briefly describe the appropriate statistical strategy that you are going to use to address this problem and explain why Question 2 does not require any calculations Hint to successfully pick the correct statistical analysis to analyze the data keep in mind things such as how many groups group means you are comparing and how the groups relate or don t relate to each other Question 3 Perform ALL the statistical procedures necessary to develop and document and state your conclusion as learned in class about the mean differences between the two groups Question 4 Graph the mean performance of the two groups Question 5 Thoroughly explain and defend your conclusions in response to the school district s question What are you going to tell the school district about these two samples based on your analyses Explain in complete sentences and in terms a person with limited skills and understanding of

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

A person going to a party was asked to bring 5 different bags of chips Going to the store she finds 1 varieties How many different selections can she make

Bookwork code 3A Which digits replace A B and C in the boxes 54 A 3B7 C 6 3 Calculator not allowed mistakes

In parts a and b identify whether the events are disjoint independent or neither events cannot be both disjoint and independent a You and a randomly selected student from your class both earn D s in this course Odisjoint independent neither b You and your class partner both earn D s in this course independent neither Odisjoint c If two events can occur at the same time they must be independent true false

Yvetia ordered two pizzas for her family Both pizzas are rectangular The larger pizza s width is equal to the length of the smaller pizza and the larger pizza s length is twice the width of the smaller pizza The sum of the perimeters of the two pizzas is 96 inches and the sum of the areas is 288 square inches Determine the dimensions of each pizza

made by the student 6x 7 2 6x 3 7 3 x 3 10 x 3 10 x 3 10 Unit 1 Normal Distribution Please answer all parts of the question 3 A vending machine company has been receiving customer complaints about their machines not working properly A cup will slide out and be filled with quid until the cup is nearly full Customers have complained about the cup overflowing If the cup contains too much liquid a customer may get burned from a spill This dould be an expensive lawsuit for the company A cup holds 8 az a Decide a mean and standard deviation you would recommend for the company that minimizes overfill and underfill cup holds 8 oz Mean Standard Deviation b Provide appropriate graphical and numerical representations hint normal distribution curve c Please explain in words why you chose your mean and standard deviation Please explain in wo how your mean and standard deviation minimize decrease the chance of overfill and underfill

Unit 3 Radical Functions Please answer all parts of the question 1 Consider the function f x graphed to the right f x x 1 2 44 t a Given avx h k How does a h and k transform the graph Explain in words and include a h and k in your answer b Determine the domain and range of the above function Record your answer usi interval notation Domain Range

Question 4 of 7 4 Suppose a simple random sample of size 70 is selected from a population of size 1 644 in which 16 of the individuals have a characteristic of interest If the sampling distribution of p is constructed what is the standard deviation of p In other words what is the value of 0 P Round your answer to the nearest thousandths Answer Continue Reset answer

Steps At a restaurant the cheeseburger has 35 less calories than 3 side salads Two burgers and a salad have a total of 945 calories How many calories are in each item Write your system Does your system have one variable isolated yes substitute isolated variable with expression solve plug in value of the variable into one equation solve for 2nd variable check in both equations does your solution work in both no isolate one variable solution ist variable solution 2nd variable

Question 2 of 7 2 Consider the small population 3 3 4 4 5 How many of the possible simple random samples of size 2 from this population result in a sample mean of 4 Answer Continue Reset answer

A drug test is accurate 98 of the time If the test is given to 1800 people who have not taken drugs what is the probability that at most 38 will test positive Probability Give your answers to at least 3 decimal places

5 and p 0 24 Next record the mean and Construct a Binomial probability distrubtion table using n standard deviation of the distribution below Where necessary round all numbers to four decimal places P x

Assume that a procedure yields a binomial distribution with a trial repeated n 20 times Use either the binomial probability formula or technology to find the probability of k 9 successes given the probability p 46 of success on a single trial Report answer accurate to 4 decimal places P X k

5 and p 0 2 Next record the mean and Construct a Binomial probability distrubtion table using n standard deviation of the distribution below Where necessary round all numbers to four decimal places P x fl x

0 1 0 05 0 2 0 05 0 6 0 2 5 10 12 Find the expected value of the above random variable

0 05 0 15 0 2 0 3 0 1 0 2 0 3 4 5 8 11 Find the expected value of the above random variable

Suppose that a box contains 7 cameras and that 5 of them are defective A sample of 2 cameras is selected at random Define the random variable X as the number of defective cameras in the sample Write the probability distribution for X k P X k What is the expected value of X

About 7 of the population has a particular genetic mutation 500 people are rando Find the mean for the number of people with the genetic mutation in such groups of 500

In a group of 20 batteries 6 are dead You choose 2 batteries at random a Create a probability model for the number of good batteries you get b What s the expected number of good ones you get c What s the standard deviation a Create a probability model Number good P Number good Round to three decimal places as needed 0 1 b The expected number of good batteries is Round to two decimal places as needed c The standard deviation is Round to two decimal places as needed 2 ose gc bu

me following data represent soll water content percentage of water by volume for Independent random samples of soll taken from two experimental fields growing bell peppers Soll water content from field I x n 72 15 1 11 2 10 3 10 8 16 6 8 3 9 1 12 3 9 1 14 3 10 7 16 1 10 2 15 2 8 9 9 5 9 6 11 3 14 0 11 3 15 6 11 2 13 8 9 0 8 4 8 2 12 0 13 9 11 6 16 0 9 6 11 4 8 4 8 0 14 1 10 9 13 2 13 8 14 6 10 2 11 5 13 1 14 7 12 5 10 2 11 8 11 0 12 7 10 3 10 8 11 0 12 6 10 8 9 6 11 5 10 6 11 7 10 1 9 7 9 7 11 2 9 8 10 3 11 9 9 7 11 3 10 4 12 0 11 0 10 7 8 6 11 2 Soil water content from field II x n 80 9 2 12 3 10 2 13 6 8 1 13 5 14 1 8 9 13 9 7 5 12 6 13 9 8 4 13 4 7 1 12 4 14 3 8 4 13 2 7 3 11 3 13 8 7 5 13 3 8 0 11 3 12 6 7 7 13 2 13 9 10 4 12 9 8 9 12 9 7 8 11 8 7 7 8 1 7 3 14 9 12 2 7 6 8 9 9 9 26 0 7 3 7 4 9 7 12 3 6 9 7 6 7 6 7 5 6 8 7 4 11 7 11 8 7 7 7 6 10 7 10 7 10 9 12 5 11 3 10 7 13 2 7 7 9 7 9 7 11 4 11 9 13 4 9 2 13 4 8 8 11 9 7 1 8 7 14 0 14 1 a Use a calculator with mean and standard deviation keys to calculate x S X and S Round your answers to four decimal places X 11 0361 X 1 2 0029 X 10 1900 2 2 6469 XXXX

7 A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red She estimates the probability model for the number of red lights she hits as shown below Complete parts a a X of red 0 3 P X x 0 04 0 16 a How many red lights should she expect to hit each day The commuter should expect to hit Round to one decimal place as needed b What s the standard deviation 1 0 24 2 0 34 4 0 15 5 0 07 red lights each day D The standard deviation is Round the final answer to one decimal place as needed Round all intermediate values to three decimal places as needed

GRAPHING SQUARE ROOT FUNCTIONS 6 S x x 5 7 f x x 1 4 8 f x 3 x 1 9 f x x 2 3 Graph each function Identify the key characteristic D Endpoint End Behavior As x As x Increasing Interval s Decreasing Interval s D Endpoint End Behavior AS X As x D Increasing Interval s Decreasing Interval s Endpoint f x f x f x f x D End Behavior As x f x As x f x Endpoint R Increasing Interval s Decreasing Interval s R End Behavior As x f x As x f x Increasing Interval s Decreasing Interval s Gina Wilson All Things Algebra LLC 2015 2

A small software company bids on two contracts It anticipates a profit of 30 000 if it gets the lan company estimates that there is a 35 chance it will get the larger contract and a 61 chance it will get the smaller contract If the company does not get either contract it will neither gain nor lose money Assuming the contracts will be awarded independently what s the expected profit E X CICCEID

The manufacturer of a sports car claims that the fuel Injection system lasts 48 months before it needs to be replaced A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced The ages of the cars at the time of replacement were in months 23 44 47 48 53 46 30 51 42 52 USE SALT 1 Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s Round your answers to four decimal places x months x 44 2000 8 1993 x months II Test the claim that the fuel injection system lasts less than an average of 48 months before needing replacement Use a 5 level of significance What are we testing in this problem

A research group conducted an extensive survey of 3179 wage and salaried workers on Issues ranging from relationships with their bosses to household chores The data were gathered through hour long telephone interviews with a nationally representative sample In response to the question What does success mean to you 1511 responded Personal satisfaction from doing a good job Let p be the population proportion of wage and salaried workers who would respond the same way to the stated question How large a sample is needed if we wish to be 95 confident that the sample percentage of those equating success with personal satisfaction is within 2 5 of the population percentage Hint Use p 0 48 as a preliminary estimate Round your answer up to the nearest whole number USE SALT

Many people consider their smart phone to be essentiall Communication news Internet entertainment photos and just keeping current are all conveniently possible with a smart phone However the battery better be charged or the phone is useless Battery life of course depends on the frequency duration and type of use One study involving heavy use of the phones showed the mean of the battery life to be 12 75 hours with a standard deviation of 2 3 hours Then the battery needs to be recharged Assume the battery life between charges is normally distributed AUSE SALT a Find the probability that with heavy use the battery life exceeds 13 hours Round your answer to four decimal places b You are planning your recharging schedule so that the probability your phone will die is no more than 5 After how many hours should you plan to recharge your phone Round your answer to the nearest tenth of an hour hours

5 A basketball announcer suggests that a certain player is streaky That is the announcer believes that if the player makes a shot the player is more likely to make the next shot As evidence the announcer points to a recent game where the player took 30 shots and had a streak of 10 made shots in a row Is this convincing evidence of streaky shooting by the player Assume that this player makes 50 of the shots and that the results of a shot do not depend on previous shots a Describe how you would carry out a simulation to estimate the probability that a 50 shooter who takes 30 shots in a game would have a streak of 10 or more made shots Do not perform the simulation b The dotplot displays the results of 50 simulated games in which this player took 30 shots What conclusion would you draw about whether this player was streaky Explain uh Longest Streak in Simulated Game 10 6 A statistics class asked an SRS of 100 students at their school whether they regularly recycle or not In the sample 55 students said that they recycle Is this convincing evidence that more than half of the students at the school would say they regularly recycle The dotplot shows the results of taking 200 SRSS of 100 students from a population in which the true proportion who recycle is 0 50 38 40 42 44 46 45 50 52 54 56 58 Simulated proportion who say Yes as a percent a Explain why the sample result 55 out of 100 said Yes does not give convincing evidence that more than half of the school s students recycle b Suppose instead that 63 students in the class s sample had said Yes Explain why this result would give convincing evidence that a majority of the school s students recycle

The Wind Mountain archaeological site is located in southwestern New Mexico Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi A random sample of excavations at Wind Mountain gave the following depths in centimeters from present day surface grade to the location of significant archaeological artifacts 85 45 120 80 75 55 65 60 65 95 90 70 75 65 68 USE SALT a Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s Round your answers to four decimal places X S cm cm b Compute a 98 confidence interval for the mean depth u at which archaeological artifacts from the Wind Mountain excavation site can be found Round your answers to one decimal place lower limit upper limit cm cm

A large tank of fish from a hatchery is being delivered to a lake The hatchery claims that the mean length of fish in the tank is 15 inches and the standard deviation is 2 inches A random sample of 39 fish is taken from the tank Let x be the mean sample length of these fish What is the probability that x is within 0 5 inch of the claimed population mean Round your answer to four decimal places USE SALT

Express Courier Service has found that the delivery time for packages is normally distributed with mean 14 hours and standard deviation 3 hours USE SALT a For a package selected at random what is the probability that it will be delivered in 18 hours or less Round your answer to four decimal places b What should be the guaranteed delivery time on all packages in order to be 95 sure that the package will be delivered before this time Hint Note that 5 of the packages will be delivered at a time the guaranteed time period Round your answer to one decimal place hr

Three circle red on white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wind Mountain archaeological site At one excavation a sample of 170 potsherds indicated that 70 were of the three circle red on white pattern How many ceramic potsherds must be found and identified if we are to be 95 confident that the sample proportion p of such potsherds is within 6 6 of the population proportion o three circle red on white patterns found at this excavation site Round your answer up to the nearest whole number USE SALT

2 A husband a wife decide to have children until they have at least one child of each gender The couple had seven girls in a row Their doctor assured them that they were much more likely to have a boy for their next child after all those girls Explain why the doctor is wrong 3 According to The Book of Odds the probability that a randomly selected U S adult drinks coffee on a given day is 0 56 a Explain what this probability means b If a researcher surveys 100 U S adults at random on the same day will exactly 56 of them have consumed coffee that day Explain 4 A very good professional baseball player gets a hit about 35 of the time over an entire season After the player failed to hit safely in six straight at bats a TV commentator said He is due for a hit by the law of averages Explain why the commentator is wrong

Abigail Bobby Carlos DeAnna and Emily go to the bagel shop for lunch every Thursday Each time they randomly pick 2 o the group to pay for lunch by drawing names from a hat Find the probability that Carlos or DeAnna or both ends up paying for lunch OP Carlos or DeAnna 7 10 0 70 OP Carlos or DeAnna 6 10 0 60 OP Carlos or DeAnna 4 10 0 40 OP Carlos or DeAnna 3 10 0 30 OP Carlos or DeAnna 5 10 0 50

According to The Book of Odds the probability that a randomly selected U S adult usually eats breakfast is 61 a Explain what probability 0 61 means in this setting b Does this probability say that if 100 U S adults are chosen at random exactly 61 of them usually eat breakfast Explain

Canada has two official languages English and French Choose a Canadian at random and ask What is your mother tongue Here is a distribution of responses combining many separate languages from the broad Asia Pacific region 5 Language English French Probability 0 63 0 22 Asian Pacific Other 0 06 0 09 Is this a valid probability model Why or why not Yes because all the probabilities sum to 1 Yes because each probability is between 0 and I and all the probabilities sum to 1 O No because this is not a complete list of the languages spoken in Canada No because all the probabilities do not sum to 1 Yes because each probability is between 0 and 1

5 A teacher uses a program that randomly chooses a student in the class to volunteer to answer a question The teacher will stop choosing students once a student gets the right answer but if the teacher is given four wrong answers in a row he will stop and help the class himself He estimates that 79 of the students in the class know the correct answer Assume that students are chosen with replacement Complete parts a through c below a Create a probability model for the number of students the teacher will call on until he receives the correct answer or stops to help the class Number of students 1 2 3 4 Probability Type integers or decimals Do not round b Find the expected number of students called on The expected number of students called on is Round to two decimal places as needed c Find the expected number of wrong answers that will be offered The expected number of wrong answers offered is Round to two decimal places as needed

You may need to use the appropriate appendix table or technology to answer this question In a campaign to eliminate non returnable beverage containers a poll of 600 voters showed 270 of them opposed the container control bill Develop a 92 confidence interval estimate for th proportion of all the voters who opposed this bill Round your answers to three decimal places to

You may need to use the appropriate appendix table or technology to answer this question A simple random sample of 800 elements generates a sample proportion p 0 80 Round your answers to four decimal places a Provide a 90 confidence interval for the population proportion to b Provide a 95 confidence interval for the population proportion to Need Help Read It

You may need to use the appropriate appendix table or technology to answer this question Fewer young people are driving In year A 66 9 of people under 20 years old who were eligible had a driver s license Twenty years later in year B that percentage had dropped to 48 7 Suppose these results are based on a random sample of 1 700 people under 20 years old who were eligible to have a driver s license in year A and again in year B a At 95 confidence what is the margin of error of the number of eligible people under 20 years old who had a driver s license in year A Round your answer to four decimal places At 95 confidence what is the interval estimate of the number of eligible people under 20 years old who had a driver s license in year A Round your answers to four decimal places to b At 95 confidence what is the margin of error of the number of eligible people under 20 years old who had a driver s license in year B Round your answer to four decimal places At 95 confidence what is the interval estimate of the number of eligible people under 20 years old who had a driver s license in year B Round your answers to four decimal places to

You may need to use the appropriate appendix table or technology to answer this question For many years businesses have struggled with the rising cost of health care But recently the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits A recent survey showed that 64 of employers are likely to require higher employee contributions for health care coverage this year relative to last year Suppose the survey was based on a sample of 600 companies likely to require higher employee contributions for health care coverage this year relative to last year At 95 confidence compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage Round your answer to four decimal places Compute a 95 confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage Round your answers to four decimal places to