Statistics Questions

Assume that a randomly selected subject is given a bone density test Those test scores are normally distributed with a mea of 0 and a standard deviation of 1 Find the probability that a given score is between 2 02 and 3 89 and draw a sketch of the region Sketch the region Choose the correct graph below A 2 02 3 89 B 2 02 3 89 Q Q O C 2 02 3 89 Q Q O D 2 02 3 89

Find the indicated area under the curve of the standard normal distribution then convert it to a percentage and fill in the blank About of the area is between z 2 and z 2 or within 2 standard deviations of the mean About of the area is between z 2 and z 2 or within 2 standard deviations of the mean Round to two decimal places as needed

Assume that a randomly selected subject is given a bone density test Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 Find the probability that a given score is less than 1 08 and draw a sketch of the region Sketch the region Choose the correct graph below O A 1 08 5 OB 1 08 O C 1 08 O D 1 08 1 08 Q Q

Assume that a randomly selected subject is given a bone density test Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 Draw a graph and find the probability of a bone density test score greater than 1 61 Sketch the region Choose the correct graph below O A 1 61 G B 1 61 Q O C 1 61 Q G D 1 61 1 61 Q Q N

Find the area of the shaded region The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 The area of the shaded region is Z 1 04 al place as needed

Find the indicated z score The graph depicts the standard normal distribution with mean 0 and standard deviation 1 0 2912 The indicated z score is Round to two decimal places as needed ZO

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes Find the probability that a randomly selected passenger has a waiting time greater than 3 25 minutes Find the probability that a randomly selected passenger has a waiting time greater than 3 25 minutes Simplify your answer Round to three decimal places as needed

Given a normal population whose mean is 670 and whose standard deviation is 37 find each of the following A The probability that a random sample of 7 has a mean between 672 and 683 Probability B The probability that a random sample of 17 has a mean between 672 and 683 Probability C The probability that a random sample of 30 has a mean between 672 and 683 Probability

Cans of regular Coke are labeled as containing 12 oz Statistics students weighed the contents of 5 randomly chosen cans and found the mean weight to be 12 1 ounces Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12 00 oz and a standard deviation of 0 12 oz Find the probability that a sample of 5 cans will have a mean amount of at least 12 1 oz

Assume that women s weights are normally distributed with a mean given by 143 lb and a standard deviation given by o 29 lb a If 1 woman is randomly selected find the probabity that her weight is between 113 lb and 176 lb b If 6 women are randomly selected find the probability that they have a mean weight between 113 lb and 176 lb c If 58 women are randomly selected find the probability that they have a mean weight between 113 lb and 176 lb

Suppose that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1 00 C If 6 of the thermometers are rejected because they have readings that are too low but all other thermometers are acceptable find the reading that separates the rejected thermometers from the others

Scores for men on the verbal portion of the SAT I test are normally distributed with a mean of 509 and a standard deviation of 112 a If 1 man is randomly selected find the probability that his score is at least 576 5 b If 12 men are randomly selected find the probability that their mean score is at least 576 5 12 randomly selected men were given a review course before taking the SAT test If their mean score is 576 5 is there a strong evidence to support the claim that the course is actually effective Enter YES or NO

Suppose that X is normally distributed with mean 80 and standard deviation 29 A What is the probability that X is greater than 124 66 Probability B What value of X does only the top 16 exceed X

The combined math and verbal scores for students taking a national standardized examination for college admission is normally distributed with a mean of 750 and a standard deviation of 160 If a college requires a student to be in the top 40 of students taking this test what is the minimum score that such a student can obtain and still qualify for admission at the college answer round to the nearest integer

Your dinner bill for Monday evening is 22 79 but you went with Mr Van Duyn who got you a 10 military discount You leave a 20 tip and are charged 7 sales tax Your dinner bill for Tuesday evening is 23 84 but get no tip because you went with a friend instead You leave a 15 tip and are charged 6 sales tax For which meal do you pay more

Retail Price 210 Markup percent 115 Find the wholesale price of the television

699 THE BO somathe Genuine Windows Vis Home Pemum SP104 30 Fi 4GB Memory Upgrade Goist Widescreen 14 Display Ooider Black Comes Standard Personakte wth Your Choice 01 0 Colors for 40 SHOP NOW If the Dell Laptop costs 699 what is the discom Marc is receiving an additional 7 off

Rosa and her friends are eating out for dinner The bill was 45 80 They want to leave a 20 tip How much should they leave for tip

2 49 coffee after 7 sales tax OUNEIN DONITS BASKIN ROSEIMS 448 5th Ave Brooklyn N Y 11215 Store Code 340 450 08 20 10 10053 8 29AN NO ICO ORIG BLEN MOSE ST TAX1 TOTAL 000 00

d the sale price NEW MARKDOWNUGG

Question 3 6 pts The following table represents gas well completions during 1986 in North and South America Source American Gas Association 1987 Gas Facts p 50 a b c P D P N North America N South America N TOTALS P D and N P D and N P D and N P D and N P D or N P D or N P D or N P D or N Useful Formulas Rule 1 P A or B P A P B P A and B Rule 2 P A or B P A and B P A and B Rule 3 P A B P B Rule 4 P AB Dry D 14 131 404 14 535 Not dry D 31 575 2 563 34 138 P A XP BA RA XP BARA YB RA TOTALS 45 706 2 967 48 643 Note The sign means complement of an event

Question 3 6 pts The following table represents gas well completions during 1986 in North and South America Source American Gas Association 1987 Gas Facts p 50 a b c P D P N North America N South America N TOTALS P D and N P D and N P D and N P D and N P D or N P D or N P D or N P D or N Useful Formulas Rule 1 P A or B P A P B P A and B Rule 2 P A or B P A and B P A and B Rule 3 P A B P B Rule 4 P AB Dry D 14 131 404 14 535 Not dry D 31 575 2 563 34 138 P A XP BA RA XP BARA YB RA TOTALS 45 706 2 967 48 643 Note The sign means complement of an event

Dr Smith a biology professor at Bradford University has decided to give his classes a stan biology exam that is nationally normed This indicates that the normal distribution is an appropriate approximation for the probability distribution of students scores on this exam The probability distribution of students scores on this standardized exam can be estimated using the normal distribution shown below e D 70 86 1 State the mean of the distribution of the biology exam scores 78 2 State the standard deviation of the distribution of the biology exam scores 8 points Grading Curve Option I Originally Dr Smith decides to curve his students exam grades as follows Students whose scores are at or above the 90th percentile will receive an A Students whose scores are in the 80th 89th percentiles will receive a B Students whose scores are in the 70th 79th percentiles will receive a C Students whose scores are in the 60th 69th percentiles will receive a D Students whose scores are below the 60th percentile will receive an F 3 Find the z scores that correspond to the following percentiles B 0 Inflection Point Point N 1 78 Inflection 90th percentile 80th percentile 70th percentile 60th percentile 4 Using that information find the exam scores that correspond to the curved grading scale Assume that the exam scores range from 0 to 100 Round to the nearest whole number A 100 B C X

When we think of scientific data we might think of a signal from an instrument but data can be a lot of different things The type of data a researcher collects is based on his or her research question Identify the data that could be collected to aner each of the following research auaskane luau may select the data multiple times Choose Rate of students s completion of assignments Description of phytoplankton species Test Scores Mass of precipitate Response rate How does acid in sediment affect the grow Volume of acid rate of a bean plant Absorbance of light Changes of length of leaf over time Distance Pressure How does the browning of apples differ under different temperature conditions How does adding a strong acid affect the amount of precipitate calcium oxalate that is formed from milk source of calcium ions and almonds source of oxalate ions What are the seasonal variations on phytoplankton populations in English bay How well can an automated tool detect defects bugs in students programming assignments How well do students understand calculating mean and standard deviation Mass of phytoplankton Taste of the brown part of apples under different conditions Mass of apples under different conditions Measure the surface area of the brown part of the apple Difference between manual marking of assignments and automated marking of assignments Choose Choose

The following summary of a statistical study gives a sample statistic and a margin of error Find the confidence interval and answer any additional questions In a survey of 1007 people 695 or 69 said that they voted in a particular presidential election The margin of error for this survey was 3 percentage points However actual voting records show that only 59 of all eligible voters actually did vote Does this imply that people lied when they responded in the survey Explain The confidence interval is from to Simplify your answers Use ascending order CITES

Two blocks of clay one of mass 1 00 kg and one of mass 7 00 kg undergo a completely inelastic collision Before the collision one of the blocks is at rest and the other block is moving with kinetic energy 32 0 J If the 7 00 kg block is initially at rest and the 1 00 kg block is moving what is the initial speed of the 1 00 kg block

Use the score formula z x14 O and the information below to find the value of o Round your answer to one decimal place if necessary 18 43 and 23 26

Two hockey players skating on essentially frictionless ice collide head on Madeleine of mass 65 0 kg is moving at 6 00 m s to the east just before the collision and at 3 00 m s to the west just after the collision Buffy of mass 55 0 kg is moving at 3 50 m s to the east just after the collision Find Buffy s velocity magnitude and direction just before the collision Express your answer with the appropriate units Enter positive value if Buffy is moving to the east and negative value if Buffy is moving to the west H C

For the following report about a statistical study identify if possible a the population b the population parameter of interest c the sampling frame d the sample e the sampling method including whether or not randomization was employed f who if anyone was left out of the study and g any potential sources of bias you can detect and any problems you see in generalizing to the population of interest Researchers waited outside a bar they had randomly selected from a list of such establishments They rolled a twenty sided die and it came up 3 so they stopped the third adult who came out of the bar then every 15th adult after that and asked whether they thought drinking and driving was a serious problem a What is the population OA The population is all bars OB The population is the adults who came out of the bar OC The population is all adults who would visit a bar OD The population is the adults in the bar OE The population for the study is unclear b What is the population parameter of interest BERICH

Suppose a poll of 892 adults asked whether increasing domestic energy production or protecting the environment should be given a higher priority The results are shown to the right Suppose we select three people at random from this sample Complete parts a through d below a What is the probability that all three responded Protect environment Round to three decimal places as needed b What is the probability that none responded Equally Important Round to three decimal places as needed c What assumption must be made to compute these probabilities This question 2 point s possible OA The events occur simultaneously B The order of the events does not matter Submit test Response Increase production 408 Protect environment 404 42 Equally important No opinion Total 38 892 Number E

Suppose a poll of 892 adults asked whether increasing domestic energy production or protecting the environment should be given a higher priority The results are shown to the right Suppose we select three people at random from this sample Complete parts a through d below c What assumption must be made to compute these probabilities OA The events occur simultaneously OB The order of the events does not matter OC The events are disjoint OD The events are independent d Explain why that assumption is reasonable OA The people were selected at random Response Increase production 408 Protect environment 404 Equally important 42 No opinion Total 38 892 Number

The Mars company says that before the introduction of purple yellow candies made up 20 of their plain M M s red another 20 and orange blue and green each made up 10 The rest were brown Complete parts a and b a Suppose you pick an M M at random 1 What is the probability that this M M is brown 2 What is the probability that this M M is orange or green 3 What is the probability that this M M is not red 4 What is the probability that this M M is striped 1 The probability that the M M is brown is Type an integer or a decimal Do not round 2 The probability that the M M is orange or green is Type an integer or a decimal Do not round Submit test 3 The probability that the M M is not red is Type an integer or a decimal Do not round 4 The probability that the M M is striped is

For the following report about a statistical study identify if possible a the population b the population parameter of interest c the sampling frame d the sample e the sampling method including whether or not randomization was employed f who if anyone was left out of the study and g any potential sources of bias you can detect and any problems you see in generalizing to the population of interest A company packaging sugar candy maintains quality control by randomly selecting 15 cases from each day s production and weighing the bags Then they open five random bags from each case and inspect the contents a What is the population OA The employees that produce sugar candy at the company OB Consumers who eat sugar candy produced by the company OC Bags of sugar candy produced by the company OD The 75 total bags that are opened from the selected cases OE The population for this study is unclear b What is the population parameter of interest A The proportion of noonle who do not not sugar candy Submit test

As mentioned in the chapter opinion polling organizations contact their respondents by sampling random telephone numbers Although interviewers now can reach about 45 8 of U S households the percentage of those contacted who agree to cooperate with the survey has fallen from 43 2 in 1997 to only 6 3 in 2018 Pew Research Center Each household selected of course is independent of the others a What is the probability that the next house will be contacted and refuse to cooperate b What is the probability in 2018 of failing to contact a house or making contact and not getting them to agree to the interview c Show reasonable ways to calculate the probability in part b a The probability that the next house will be contacted and refuse to cooperate is Type an integer or a decimal rounded to four decimal places b The probability of failing to contact a house or making contact and not getting them to agree to the interview is Type an integer or a decimal rounded to for decimal places c Show reasonable ways to calculate the probability in part b Select all that apply Submit test A P contacted n not agree x 1 P contacted B P contacted n not agree 1 P contacted

9 pts According to a study 67 of cars are some shade of grey white black grey or silver If we take a random sample of 25 cars find the following probabilities a None of them are a shade of gray 1 0 67 0 33 b All of them are a shade of gray 67 0 67 c Exactly 15 of them are a shade of gray 15 0 67 0 402 d Less than 10 of them are a shade of gray 0 0015 e At least 13 of them are a shade of gray 1 0 038 0 962 f How many cars would we expect to be a shade of gray don t forget units

An amusement park has opened a new roller coaster It is so popular that people are waiting for up to 3 hours for a 2 minute ride Concerned about how patrons who paid a large amount to enter the park and ride on the rides feel about this they survey every 15th male as they exit the park starting from a randomly selected male Complete parts a through d below OA Yes the sample is likely to be representative of everyone in the park OB No the sample is not likely to be representative of everyone who waited in line for the roller coaster OC No the sample is not likely to be representative of everyone in the park OD Yes the sample is likely to be representative of everyone who waited in line for the roller coaster d What members of the population of interest are omitted Submit test O A no members of the population of interest are omitted B amusement park employees OC the patrons who are not willing to wait in line for the ride D female patrons

An amusement park has opened a new roller coaster It is so popular that people are waiting for up to 3 hours for a 2 minute ride Concerned about how patrons who paid a large amount to enter the park and ride on the rides feel about this they survey every 15th male as they exit the park starting from a randomly selected male Complete parts a through d below b vvnat is the sampling frame OA all the male patrons of the park OB all the males who go to amusement parks OC all the male patrons who like roller coasters OD all the patrons of the park c is the sample likely to be representative of the population of interest OA Yes the sample is likely to be representative of everyone in the park OB No the sample is not likely to be representative of everyone who waited in line for the roller coaster OC No the sample is not likely to be representative of everyone in the park On Vor the comple is likely to ho ropocentative of overwone who waited in line for the roller coaster

1 10 pts We bought a pack of 10 lightbulbs from a garage sale and collect a random sample of 2 lightbulbs no replacement and count the number of lightbulbs that are defective create a probability distribution for this discrete random variable a First define your random variable X the number of defective lightbulbs in a random The random variable X will be defined sample of 2 lightbulbs chosen without replacement from the pack of 10 bulbs X can take from values 0 to 2 where X 0 means both bulbs are working X 1 means one bulbs is working and X 2 means both bulbs are defective b Next showing work for all of your probabilities in the space below fill in the table below round probabilities to 4 decimal places X P X total of bulbs 10 of defective bulbs 6 of working bulbs 4 402 probability of 2 bulbs working 10 probability of 1 bulbs working probability c What do the probabilities sum up to P x 2 7 5 0 1333 6c 4c 10 6c2 of 2 bulbs working 10c 10C2 0 5333 0 6666 1 1999 33 15 1 0 5333 2 0 3333 0 3333 I Sum 1 P x 1 1 1 28 27 28 1 1 3 1 1 28 P x 0 2 ts d What is the expected number of defective lightbulbs in our sample P x 2 0 3333 0 3333 2 0 53331 0 1333 0 P x 1 0 5333 P x 0 0 1333 0 1333 0 5333 1 11 2 defective lightbulbs e Using technology find the standard deviation for the number of defective lightbulbs in our sample

Here are several scatterplots The calculated correlations are 0 951 0 736 0 021 and 0 923 Which is which Match each scatterplot with its calculated correlation a b c a c b d

C This question 2 point s possible In 1978 a popular science magazine reported that a study of women in Australia indicated that having sons shortened the lifespans of mothers by about 47 weeks per son but that daughters helped to lengthen the mothers lives The data came from church records from the period 1605 to 1887 Answer parts a through e below OA The parameter of interest is difference in average lifespan between sons and daughters OB The parameter of interest is difference in average lifespan between mothers of sons and mothers of daughters OC The parameter of interest is average numbers of sons and daughters OD The parameter of interest is difference in average lifespan of mothers in Australia e Identify the nature and scope of the conclusion regarding what the results may or may not indicate Submit test OA For this group having sons was associated with a decrease in lifespan of an average of 47 weeks per son while having daughters was associated with an unspecified increase in lifespan Without random assignment there is no way to know that having sons caused a decrease in lifespan OB For this group having children was associated with a decrease in lifespan of an average of 47 weeks per child Without random assignment there is no way to know that having sons caused a decrease in lifespan OC For this group having daughters was associated with an increase in lifespan of an average of 47 weeks per daughter while having sons was associated with an unspecified decrease in lifespan

An amusement park has opened a new roller coaster It is so popular that people are waiting for up to 3 hours for a 2 minute ride Concerned about how patrons who paid a large amount to enter the park and ride on the rides feel about this they survey every 15th male as they exit the park starting from a randomly selected male Complete parts a through d below c Is the sample likely to be representative of the population of interest OA Yes the sample is likely to be representative of everyone in the park OB No the sample is not likely to be representative of everyone who waited in line for the roller coaster OC No the sample is not likely to be representative of everyone in the park OD Yes the sample is likely to be representative of everyone who waited in line for the roller coaster d What members of the population of interest are omitted Submit test OA no members of the population of interest are omitted OB amusement park employees OC the patrons who are not willing to wait in line for the ride

For many people breakfast cereal is an important source of fiber in their diets Cereals also contain potassium a mineral shown to be associated with maintaining a healthy blood pressure An analysis of the amount of fiber in grams and the potassium content in milligrams in servings of 77 breakfast cereals produced the regression model Potassium 39 26Fiber If your cereal provides 10 grams of fiber per serving how much potassium does the model estimate you will get milligrams of potassium

A humor piece published in a reputable medical journal notes that people can t tell for sure whether parachutes are safe and effective because there has never been a properly randomized double blind placebo controlled study of parachute effectiveness in skydiving Suppose a researcher were designing such a study Complete parts a through h below a What is the factor in this experiment OA Jumping with or without a parachute OB The parachutes OC The skydivers OD How the parachutes are distributed to the skydivers b What experimental units should be used OA Airplanes B Different brands of parachutes OC The research team Romaining 02 08 09 Next

in 1978 a popular science magazine reported that a study of women in Australia indicated that having sons shortened the lifespans of mothers by about 47 weeks per son but that daughters helped to lengthen the mothers lives The data came from church records from the period 1605 to 1887 Answer parts a through e below a Identify whether the above research is an observational study or an experiment The described research is an b Was the study retrospective or prospective observational study This is a c Identify The subje How were retrospective prospective d how they were selected 2 OA T www or the study OR The women were randomly selected

In a study of streams in the Adirondack Mountains the following relationship was found between the water s pH and its hardness measured in grains Is it appropriate to summarize the strength of association with a correlation E 8 0 7 6 72 6 8 64 125 250 Hardness grains Choose the correct answer below OA All the conditions for correlation are met OB The scatterplot is not linear correlation is not appropriate OC The scatterplot has outliers correlation is not appropriate OD The variables are not quantitative correlation is not appropriate 500

Are fat and calories in fast food related Here are the fat and calorie data for several brands of burgers Analyze the association between fat content and calories using correlation and scatterplots Fat g Calories O A Calories 700 T 23 426 300 10 Make a scatterplot for the data Choose the correct answer below F Fat g 50 32 584 5 33 588 37 567 OB What is the correlation coefficient for the data Calories 700 40 641 300 10 IC B Fat g 40 677 50 Q Q 44 660 O C Calories 700 T 300 10 Fat g 50 o O D Calories 700 300 10 F Fat g 50 O

Which of the scatterplots to the right show a little or no association b a negative association c a linear association d a weak or moderately strong association e a very strong association a Which scatterplot s show s little or no association OA All of these scatterplots OB 1 1 3 2

Is there an association between time of year and the nighttime temperature in North Dakota A researcher assigned the numbers 1 365 to the days January 1 December 31 and recorded the temperature at 2 00 a m for each What might you expect the correlation between DayNumber and Temperature to be Explain Choose the correct answer below SCIEB OA Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since there is a clear pattern the correlation should be near 1 OB Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since the relationship is not linear the correlation should be near 0 OC Temperatures should be low in January increase through spring and into the summer months and then decrease again in the fall and winter Since there is a clear pattern the correlation should be near 1 O D Temperatures should be low in January and then increase throughout the rest of the year Since the relationship is positive and linear the correlation should be near 1

9 pts According to a study 67 of cars are some shade of grey white black grey or silver If we take a random sample of 25 cars find the following probabilities a None of them are a shade of gray 1 0 67 0 33 b All of them are a shade of gray 67 0 67 c Exactly 15 of them are a shade of gray

An analysis of the amount of fiber in grams and the potassium content in milligrams in servings of 77 breakfast cereals produced the regression model Potassium 35 24Fiber Explain what the slope means Choose the correct answer below Submit test OA The model predicts that cereals will have approximately 35 more grams of fiber for every additional milligram of potassium OB The model predicts that cereals will have approximately 35 more milligrams of potassium for every additional gram of fiber OC The model predicts that cereals will have approximately 24 more milligrams of potassium for every additional gram of fiber OD The model predicts that cereals will have approximately 24 more grams of fiber for every additional milligram of potassium