Stats final cert
alarm system 3 different alarm system each probability of 0.86
1-0.86= 0.14 .14^3 = 0.002744 1-0.002744= 0.997256
Wanda Wooden widgets; average defects On average, how many defects are found? 0= 0.50 1= 0.25 2= 0.15 3= 0.06 4= 0.03 5= 0.01
(0 x 0.50)+ (1 x 0.25)+(2 x 0.15)+(3 x 0.06)+(4 x 0.03)+(5 x 0.01)= 0.9
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years. Round your answer to three decimal places.
(0.163, 0.189)
In 2015 as part of the General Social Survey, 1388 randomly selected American adults responded to this question: "Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?" Of the respondents, 458 replied that America is doing about the right amount. What is the 95% confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment.
(0.305, 0.355)
The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Suppose we take a poll (random sample) of 3865 students classified as Juniors and find that 3083 of them believe that they will find a job immediately after graduation. What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.
(0.781, 0.814)
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .2005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval? Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean? Round answers to four decimal places
(15.8495,16.2505)
Which of the following scenarios are Binomial?
-An engineer chooses a SRS of 10 switches from a shipment of 10,000 switches. Suppose 10% of the switches in the shipment are bad. The engineer counts the number X of bad switches in the sample. -You observe the sex of the next 20 children born at a local hospital: X is the number of girls among them.
Continuous example
-avg weight of students in class -avg age of student in class -students GPA -back waist length -foot length
Let A and B be two disjoint events such that P(A) = 0.06 and P(B) = 0.11. What is P(A and B)?
0
A club is choosing 2 members to serve on a committee. The club has nominated 4 women and 2 men. Based on chance alone, what is the probability no women are chosen to be on the committee?
0.0667
An automobile dealer gathered data concerning the age and the type of vehicle that was purchased from a random sample of the people that bought vehicles from them in the past year. The data is contained in the table below. 20-39 years 40-59 years 60 years and older Total Truck 25 15 10 50 Car 10 20 10 40 SUV 12 17 35 64 Total 47 52 55 154 Suppose a buyer is selected at random from this group, what is the probability that the buyer is in the age group 40 - 59 and purchased an SUV? (The responses below are rounded to 4 decimals.)
0.1104
If P(A) = 0.47, P(B) = 0.86, and P(A and B) = 0.11, then P(A|B) =
0.13
Let A and B be two independent events such that P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?
0.18
If P(A) = 0.38, P(B) = 0.14, and P(A and B) = 0.03, then P(A|B) =
0.21
Let A and B be two disjoint events such that P(A) = 0.24 and P(B) = 0.51. What is P(A or B)?
0.24+0.52=0.75
In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?
0.25
According the the Pew Research Center, the probability of a randomly selected person living in the United States identifying with a particular religious affiliation—Protestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")—is shown in the following chart. Affiliation Protestant Christian Catholic Christian Other Christian Non-Christian Unaffiliated "none" Probability 0.466 0.208 0.033 0.06 0.233 Adapted from "America's Changing Religious Landscape," Pew Research Center, May 12, 2015, http://www.pewforum.org/religious-landscape-study/state/california/ Assuming this data is accurate and stable, what is the probability that a randomly selected person living in the United States would not identify as Christian?
0.293
according the the Pew Research Center, the probability of a randomly selected person living the United States identifying with a particular religious affiliation—Protestant Christian; Catholic Christian, Other Christian, Non-Christian (including Jewish, Muslim, Buddhist, Hindu and other religions); and Unaffiliated (the so-called "nones")—is shown in the following chart. Affiliation Protestant Christian Catholic Christian Other Christian Non-Christian Unaffiliated "none" Probability 0.466 0.208 0.033 0.06 0.233 Adapted from "America's Changing Religious Landscape," Pew Research Center, May 12, 2015, http://www.pewforum.org/religious-landscape-study/state/california/ Assuming this data is accurate and stable, what is the probability that a randomly selected Christian living in the United States would identify as Catholic?
0.294
Dogs are inbred for such desirable characteristics as blue eye color, but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) If a Dalmatian has blue eyes, there is a 42% chance that it is deaf. What is the probability that a randomly chosen Dalmatian is blue-eyed and deaf?
0.31 * 0.42 = 0.1302
At a dental office, the probability a patient needs a cleaning is 0.6. The probability a patient needs a filling is 0.32. Assuming the events "needs a cleaning" and "needs a filling" are independent, then what is the probability a patient needs a filling given that he/she needs a cleaning?
0.32
Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. Denote this by H (the remaining were away games). Of all the games, 25% were wins. Denote this by W (the remaining were losses). Of all the games, 20% were at-home wins. Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)
0.33
At a dental office, the probability a patient needs a cleaning is 0.67. The probability a patient needs a filling is 0.34. Assuming the events "needs a cleaning" and "needs a filling" are independent, then what is the probability a patient needs a filling given that he/she needs a cleaning?
0.34
Suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (C). The remaining do not like chocolate. 40% of your friends sprinkles (S) topping. The remaining do not like sprinkles. 25% of your friends like chocolate (C) and also like sprinkles (S). If your friend had chocolate, how likely is it that they also had sprinkles? (Note: Some answers are rounded to 2 decimal places).
0.36
The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. Suppose a golfer played the course today. Find the probability that her score is at least 74
0.3694
Suppose that the handedness of the last 15 U.S. presidents is as follows: (i) 40% were left-handed (L) (ii) 47% were democrats (D) (iii) If a president is left-handed, there is a 13% chance that the president is a Democrat. What is the probability that a randomly chosen U.S. president is left-handed and a democrat?
0.40 * 0.13 = 0.0520
If P(A) = 0.75, P(B) = 0.11, and P(A or B) = 0.81, then P(A|B) =
0.45
Suppose your friends have the following ice cream preferences: 36% of your friends like chocolate (C). The remaining do not like chocolate. 31% of your friends like sprinkles (S) topping. The remaining do not like sprinkles. 15% of your friends like Chocolate (C) and also like sprinkles (S). Of the friends who like sprinkles, what proportion of this group likes chocolate? (Note: Answers are rounded to four decimal places.)
0.4839
Wanda's Wooden Widgets what is the probability that given shift there will be at most 2 defects? 0= 0.50 1= 0.25 2= 0.15 3= 0.06 4= 0.03 5= 0.01
0.50+0.25+0.15= 0.90
A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 4 men. Based on chance alone, what is the probability that one woman and one man will be chosen to be on the committee?
0.5333
The random variable X, representing the number of items sold in a week, has the following probability distribution: x 0 1 2 3 4 5 6 P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 By the fourth day of a particular week, 3 items have already sold. What is the probability that there will be less than a total of 5 items sold during that week?
0.67
Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. Denote this by H (the remaining were away games). Of all the games, 25% owere wins. Denote this by W (the remaining were losses). Of all the games, 20% were at-home wins. If the team won a game, how likely is it that this was a home game? (Note: Some answers are rounded to 2 decimal places.)
0.80
The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. x 0 1 2 3 4 5 P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01 After 2 hours of a particular shift, 2 defects have already been detected. What is the probability that there will be less than a total of 4 defects detected during the entire shift?
0.84
The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. x 0 1 2 3 4 5 P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01 What is the probability that in a given shift there will be at most 2 defects?
0.90
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 25 students from this distribution. What is the probability that a SRS of 25 students will spend an average of between 600 and 700 dollars? Round to five decimal places.
0.96278
The following probabilities are based on data collected from U.S. adults. Individuals are placed into a weight category based on weight, height, gender and age. Underweight Healthy Weight Overweight (not Obese) Obese Probability 0.021 0.374 0.343 0.262 Based on this data, what is the probability that a randomly selected U.S. adult is not underweight?
0.979
For a criminal trial, 8 active and 4 alternate jurors are selected. Two of the alternate jurors are male and two are female. During the trial, two of the active jurors are dismissed. The judge decides to randomly select two replacement jurors from the 4 available alternates. What is the probability that both jurors selected are female?
1/6
An urn contains 19 red marbles, 28 blue marbles, and 46 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?
19 + 28 + 46 = 93 19/93 = 0.2043
suppose joan has a fair four-sided die with sides that are numbered 1,2,3,and 4 after she rolls it 33times, joan finds that she's rolled the number 3 a total of seven times. what is the empirical probability that joan rolls a 3?
21.21%
In June 2017, a survey was conducted in which a random sample of 1440 U.S. adults was asked the following question: "In 1973 the Roe versus Wade decision established a woman's constitutional right to an abortion, at least in the first three months of pregnancy. Would you like to see the Supreme Court completely overturn its Roe versus Wade decision, or not?" The results were: Yes—29%, No—67%, Unsure—4% Which of the following is true about this scenario?
29%, 67%, and 4% are all statistics.
Pictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 30. Based on the histograms, what is the most likely value of the population mean?
3.0
an urn contains 46 marbles consisting of 11 red marbles, 32 blue marbles, and 3 yellow marbles. what is the probability of randomly selecting a yellow marble from the urn?
3/46= 7%
Pictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 40. Based on the histograms, what is the most likely value of the population mean?
8
In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?
A larger sample size gives a narrower confidence interval.
When the population is not normally distributed, the sampling distribution of the mean approximates which of the following?
A normal distribution given a large enough sample
Talkshow host "Bully" Loney asked listeners of his call in to give their opinion on a topic that he had just spent most of his program ranting about. The station got 384 calls. This is an example of what type of sample?
A voluntary response sample
the boxplots below show the real estate values of single=family homes in two neighboring cities which city has greater variability in real estate values?
Bigburg
Which of the following is a discrete data random variable?
Cars finished in a factory each day
AB rare blood type: exactly 2 of US residents have AB? 4% in Us 1.5 in Australian x= number of US with AB y= number of australian with AB exact 2 of US resident have AB? n=50 p=0.04
EXCEL: =binom.dist(2,50,0.04,0) =0.2762
surgeon completeing a laproscopic surgery to remove gall bladder u=132.4 minutes std=15.7 usually risky surgery is one that is in top 4% minimum time before becoming risky?
EXCEL: norm.inv(0.96,132.4,15.7) =159.9
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule. (a) What proportion of the students scored at least 23 points on this test, rounded to five decimal places? (b) What is the 29 percentile of the distribution of test scores, rounded to three decimal places?
Correct! At least 23 means 23 or more. The correct proportion of students is: .30854. We wish to calculate P(X ≥ 23). Since the normal distribution is continuous, we do not have to worry about the inequality signs. Excel will only calculate < or ≤ so we need to re-write the problem by using the complement rule. Thus, we can can use the Excel function = 1-Norm.Dist(x, mean, standard deviation, 1). The normal distribution will ALWAYS have a cumulative equal to 1. Part 2 Correct! The 29 percentile of the distribution of test scores is: 20.893. We can find the 29th percentile by using the Excel function =NORM.INV(0.29, mean, standard deviation).
A certain medical test is known to detect 71% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
Correct! The correct answer is: 0.0326. Let X be the number of tests that show a positive result. Thus, we want P(X=10). We can use the Excel command = binom.dist(x, n, p, 0). We must use 0 here since we are only considering x = 10. Part 2 Correct! The correct answer is: 0.4099. Let X be the number of tests that show a positive result. Thus, we want P(X ≥ 8). Excel can only calculate probabilities that are of the form ≤. We write it as follows: P(X ≥ 8) = 1- P(x ≤ 7) = 1 - binom.dist(7,10,0.71,1) Part 3 Correct! At most means 4 or less. The correct answer is: 0.0404
Suppose the scores on an exam are normally distributed with a mean μ = 75 points and standard deviation σ = 8 points. What is the exam score for an exam whose z-score is 1.25?
Correct. A z-score of 1.25 means that the actual exam score is 1.25 standard deviations above the mean, and therefore the exam score we are looking for is mean + 1.25 * SD = 75 + 1.25 * 8 = 85.
Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why. X 3 6 9 12 15 P(X=x) 4/9 2/9 1/9 1/9 1/9
Yes, the probabilities associated with each X are all positive and they all add up to 1.
An urn contains 22 red marbles, 28 blue marbles, and 40 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red or a blue marble?
For events A and B, P(A or B) = P(A) + P(B) - P(A and B). P(Red or Blue) = 22/90 + 28/90 - 0 P(Red or Blue) = 0.5556
National Longitudinal Study of Adolescent Health calculate the row percentages for participants who were obese
HORZIONTAL perc 1= perc 2= perc 3= total perc= 100(ALWAYS)
Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams. If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?
It is extremely unlikely for this to occur; the probability is very close to 0.
Which of the following is a characteristic of a discrete random variable?
It is something you count.
The following three histograms represent the probability distributions of the three random variables X, Y, and Z. Which of the three random variables has the largest standard deviation?
Z
Dogs are inbred for such desirable characteristics as blue eye color, but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) If a Dalmatian has blue eyes, there is a 42% chance that it is deaf. Based on the results of this study is "having blue eyes" independent of "being deaf"?
No, since 0.38 is not equal to 0.42.
Suppose that the handedness of the last fifteen U.S. presidents is as follows: 40% were left-handed (L) 47% were Democrats (D) If a president is left-handed, there is a 13% chance that the president is a Democrat. Based on this information on the last fifteen U.S. presidents, is "being left-handed" independent of "being a Democrat"?
No, since 0.47 is not equal to 0.13.
Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why. X 20 30 40 50 P(X=x) 1.1 0.6 .2 .1
No, while the probabilities are all positive, the P(X=20)=1.1. Probabilities cannot exceed
it is known that roughly 5% of the general population carry a certain virus. A health researcher believes that among caucasian males the percentage is actually lower. Which of the following will provide the most convincing evidence to support the researcher's suspicion?
Out of 6,000 randomly chosen caucasian males, 240 males carry the virus 240/6,000 = 0.04(4%)
Let A and B be two independent events such that P(A) = 0.13 and P(B) = 0.77. What is P(A or B)?
P(A or B) = P(A)+P(B)-P(A and B). =0.7999
Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. Denote this by H (the remaining were away games). Of all the games, 25% were wins. Denote this by W (the remaining were losses). Of all the games, 20% were at-home wins. Of the at-home games, we are interested in finding what proportion were wins. Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins?
P(W | H)
In a certain liberal arts college with about 10,000 students, 48% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?
P(same gender)=P(MM or FF) = P(MM) + P(FF) Note: the events of MM and FF are mutually exclusive, i.e., they cannot happen at the same time. The correct probability is: 0.5008
Which of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply.
The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. The distribution is normal regardless of the sample size, as long as the population distribution is normal. The distribution's mean is the same as the population mean. The distribution's standard deviation is smaller than the population standard deviation. Feedback
In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population. Let A represent the event "the first individual has diabetes." Let B represent the event "the second individual has diabetes."
TRUE
In the population, 8% of males have had a kidney stone. Suppose a medical researcher randomly selects two males from a large population. Let A represent the event "the first male has had a kidney stone." Let B represent the event "the second male has had a kidney stone." True or false? A and B are independent events.
TRUE
Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply.
The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60.
the histogram below shows the times, in minutes, requires for 25 rats in an animal behavior experiment to successfully navigate a maze. which of the following are the appropriate numerical measures to describe the center and spread of the above distribution?
The median and the IQR
Consider the following statements about a particular traditional class of statistics students at State U related to discrete and continuous variables. Which of the following is a true statement? Check all that apply.
The number of students in the class is a discrete variable. The average age of the students in the class is a continuous variable. A student's GPA is a continuous variable.
Parking survey: For a class assignment, a group of statistics students set up a table near the student parking lot. They asked students who passed by to complete a quick survey about whether they support the building of a multi-level parking structure that would add 425 new spaces at the college. They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population does the confidence interval apply?
The results do not apply to any population because this was a convenience sample.
An interactive poll on the front page of the CNN website in October 2011 asked if readers would consider voting for Herman Cain, who at the time, was a Republican presidential candidate. A statistics student used the information from the poll to calculate the 95% confidence interval. He got (0.53,0.59). He also conducted a hypothesis test. He found very strong evidence that more than half of voters would consider voting for Herman Cain. To what population do these conclusions apply?
The results do not apply to any population because this was a voluntary response sample.
Based on the limited amount of available student parking spaces on the GSU campus, students are being encouraged to ride their bikes (when appropriate). The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 129 students surveyed 7 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
The sample needs to be random but we don't know if it is. The actual count of bike riders is too small. n*^p is not greater than 10.
Concert marketing: GSU's Rialto Center for the Performing Arts wanted to investigate why ticket sales for the upcoming season significantly decreased from last year's sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail. Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail? Check all that apply.
The sample needs to be random, but we don't know if it is. The actual count of community residents who received the concert brochure by mail is too small. n^p is not greater than 10.
Suppose the American National Elections Studies agency (ANES) wishes to conduct a survey. It plans to ask a yes/no question to determine if those surveyed plan to vote for a certain candidate. One proposal is to randomly select 400 people and another proposal is to randomly select 1600 people.
The sample proportion from sample of 1,600 is more likely to be close to the true population proportion, p.
a survey was conducted to study the relationship between the annual income of a family and the amount of money the family spends on entertainment. data were collected from a random sample of 280 families from a certain metropolitan area which of the following would be meaningful display of the data from this study?
a scatterplot
For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 4 systems detects theft with a probability of 0.89 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 4 systems will detect it. What is the probability that when a theft occurs, at least oneof the 4 systems will detect it?
To find the probability of "at least one", i.e, one or more, it may be best to calculate the following:1-P(none). Before you proceed, you will, obviously, need to find the P(none) first. The correct probability in this instance is: 0.99985
here are the number of hours that 9 students spend on the computer on a typical day 1 6 7 8 11 6 12 15 the data from the aboce 9 students form what type of distribution?
Unimodal
Three random variables, U, V, W have distributions as shown in the graphs below. Which one of the three random variables has the largest standard deviation?
V
Race relations: A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% responded that race relations in this country are generally bad. The 95% confidence interval is (0.58, 0.64). Which of the following is an appropriate interpretation of the 95% confidence interval?
We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.
In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval?
We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.
Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion?
We can select a lower confidence level and increase the sample size.
The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: x 0 1 2 3 4 5 P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05 On average, how many accidents are there in the intersection in a week?
We need to find the mean of X, μx. μx = (0 * 0.20) + (1 * 0.30) + (2 * 0.20) + (3 * 0.15) + (4 * 0.10) + (5 * 0.05) = 1.8.
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
We take repeated random samples of size 15 from a population that is normally distributed. We take repeated random samples of size 50 from a population of unknown shape.
employed women have never been married 23% never married survey of 15 women a)what is the probability of EXACT 2 of them have never been married? b)Most 2 of them have never been married
a) EXCEL: binom.dist(2,15,0.23,0) =0.1858 b)EXCEL binom.dist(2,15,0.23,1) =0.2945
the boxplot below show the real estate values of single-family homes in neighboring cities which city has the greater percentages of households with real estate values above $85,000?
both cities have the same percentage of households with real estate values above $85,000
what type of variable is color?
categorical
the boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes which class has more students??
it is impossible to tell from the boxplots
probability of experiencing nausea or decrease sex drive?
p(N)+p(D)-p(N n D) 0.21+0.53 -0.11 =0.63
in order to study whether IQ level is related to birth order, data were collected from a sample of 540 students on their birth order(oldest/in between/youngest) and their score on an IQ test which of the following would be a meaningful display from this study
side by side boxplots
The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The Central Limit Theorem says that
the average burnout time of a large number of bulbs has a distribution that is close to Normal.
suppose the correlation between two variables(x,y) in a data set is determined to be r=0.83, What must be true about the slop, b, of the least-squares line estimated for the same set of data?
the slop will have the same sign as the correlation
A fair die is rolled 12 times. Consider the following four possible outcomes: (i) 5 2 6 3 2 1 4 1 6 5 3 4 (ii) 1 1 2 2 3 3 4 4 5 5 6 6 (iii) 6 6 6 6 6 6 6 6 6 6 6 6 (iv) 1 5 4 3 5 1 2 4 4 6 4 5 Which of the following is the most likely outcome: (i), (ii), (iii), (iv)?
they are all equally likely
when conducting a survey, which of the following is the most important reason to avoid using a volunteer sample?
your conclusions could not be reliably generalized to a larger population
A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment?
{F, PF, PPF, PPP}
A couple decides to have three children. Let A define the event that the couple has at least 1 girl. What are the possible outcomes for this event? (G=girl, B=boy) {G, BG, BBG}
{GGG, GGB, GBG, BGG, GBB, BGB, BBG}
A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment?
{SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF}
the distribution of IQ is approximately normal in shape with a mean of 100 and a standard deviation of 29 according to the standard deviation rule, ___% of people have an IQ between 62 and 138
95%
number of days after mailout it takes a utility company to receive payment for customer's bill is a normal random variable u=31 days sd=6 days probability is 0.997 that a bill will be received between which of the following of days?
99.7% = 3 std of mean 31-3(6)= 13 31+3(6)= 49
certain liberal arts college with 10,000 kids, 59% males. If students selected at random, what is the probability they are same gender?
=P(both male) or P(both female) (.59 x .59) + (.41 x .41) = 0.5162
lifetime in miles for tire manufacturer u=22,000 miles std=3,100 miles money back guarantee, so no more than 3% of tires will qualify for refund. Minimum # of miles manufactures can guarantee
=norm.inv(0.03,22,000,3,100) =16,170
Female competitive swimmers u=141 seconds std=7 seconds suppose fastest 6% of swimmers are offered scholarships. Swimmers shouldn't swim no more than how many seconds?
=norm.inv(0.04,11,1.5) =8.37
Medical test is known to detect disease 70% of people afflicted with disease "y" if 10 people with disease use administered what is the probability?
All 10 have the disease? EXCEL =binom.dist(10,10,0.70,0) =0.282 At least 8 have the disease? EXCEL: 1-binom.dist(7,10,0.7,1) =0.3828 At most 4 have disease? EXCEL: binom.dist(4,10,0.7,1) =0.0473
Binomial Scenarios
engineering chooses a SRS of 10 switches from shipment of 10,000 switches 10% of switches are bad you observe sex of next 20 kids born at local hospital x=number of girls
numbers of accidents in interaction how many accidents are in a week 0= 0.20 1= 0.30 2= 0.20 3= 0.15 4= 0.10 5=0.05
(0)(0.20)+(1)(0.30)+(2)(0.20)+(3)(0.15)+(4)(0.10)+(5)(0.05) =1.8
items sold in a week 3 items have been sold, what's the probability that total will be less than 5? 0= 0.10 1= 0.20 2= 0.40 3= 0.15 4= 0.05 5=0.05 6= 0.05
(0.15)(0.05)/ (0.15+0.05+0.05+0.05) =0.67
finding median
(n+1)/2 EXCEL: =median(highlight data)
when buying a home, the interest rate given on a loan typically depends on the applicant's credit score. The Fair Isaac Corporation(FICO) is a major producer of credit scores. the following table contains 10 randomly selected loan applicants along with their FICO scores and the interest rates that they were given when financing their homes. the linear correlation coefficient between FICO score and home loan interest rate is:
-0.9819
Discrete examples
-cars finish in a factory each day -number of times that a hiker walks over 8miles each day -number of students in class -shoe size -dress size
Large population of college student with math anxiety 20% of students random 10 students from population standard deviation?
/(10x 0.20)(1-0.20) =1.265
Christians Probability of selected a christian and they identify as catholic protestant= 0.466 catholic= 0.208 other= 0.033 NON= 0.06 NONE= 0.233
0.466+ 0.208+ 0.033+0.06+0.233= 0.707 0.208/0.707= 0.294
Christians and non-Christians probability of randomly selecting someone who doesn't identify as christian protestant: 0.466 catholic: 0.208 other: 0.033 NON: 0.06 No: 0.233
0.466+0.208+0.033= 0.707 1-0.707=0.293
Wanda's Wooden Widgets 2 defects are already detected. what is probability that there will be less than a total of 4 defects during the entire shift? 0= 0.50 1= 0.25 2= 0.15 3= 0.06 4= 0.03 5= 0.01
0.50+0.25+0.15= 0.9 0.9-0.06= 0.84
exam scores on exam u=75 std=8 suppose that top 4% of exams will be given an A+. In order to be given a A+ the exam must be at least?
1-0.04= 0.96----1.75 1.75 SD above mean 1.75x8= 14 75+14=89%
Golfer score u=73 std=3 probability that her score is at least 74
1-0.6305 =0.3694
Engineering school 52% male 31% students between 18-20 26% both male between 18-20 Female and not between age 18-20?
1-P(M u A) 1-(P(m)+P(a)-P(M n A) 1-(0.52+0.31-0.26) 1-0.57= 0.43
21% nausea 41% decreased sex drive 13% both probability of experiencing neither
1-p(N n D) p(n)+p(d)-p(N n D) .21+.41-.13= 0.49 1-0.49= 0.51
Test scores u=75 std=8 points what is the exam score for an exam whose score is 1.25?
1.25 x 8point=10 points 75+10 = 85%
distrubition of battery life in hours for battery model in the cell phones? normal random variables u=8 std=1.2 using standard deviation rule, how likely lasts longer than 10.4hours?
10.4 is 2 std above ,mean 1-0.95=0.05 0.05/2= 0.025
he cost of taking your pet aboard the air flight with you in the continental US varies according to the airlines. the five number summary for prices based on a sample of major US airline was min=60, Q1=100, median=110, Q3=125, max=150 if we were to build box plot for this data, the box would stretch between which two values? what would be the lowest value:___and highest:____
100; 125
there are 68 students in a film production course at GSU: 28 freshmen, 12 sophomores, 14 juniors, and 14 seniors. One student is selected at random to have his film shown at the Rialto in downtown Atlanta. What is the probability that the chosen student is a junior?
14/68= 21%
suppose joan has a fair four-sided die with sides that are numbered 1,2,3,and 4 after she rolls it 33 times, joan finds that she's rolled the number 4 total of five times. What is the empirical probability that joan rolls a 4?
15.15%
The distribution of IQ is approximately normal in shape with a mean of 100 and standard deviation of 18 according to the standard deviation, only __% of people have an IQ over 118.
16%
Value of Constant, K 0= 2k 1= 3k 2= 13k 3= 2k probability of P(X<2)
2+3=5 5/20= 0.25
an urn contains 43 marbles consisting of 10 red marbles, 30 blue marbles, and 3 yellow marbles. what is the probability of randomly selecting a blue marble from the urn?
30/43= 70%
a 2009 study analyzed data from the national longitudinal study of adolescent health. participants were followed into adulthood. each study participant was categorized as to whether they were obesse.. what percentage of those who were married were obese?
34.7%(147/424)
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 385 and standard deviation of 34 According to the standard deviation rule, approximately 95% of the students spent between _____ and ______ on textbooks in a semester
385-2(34)= $317 385+2(34)= $453
the distribution of the amount of money spent by students on textbook in a semester is approximately normal in shape with a mean of u=435 and a standard deviation of std=32 according to the standard deviation rule, almost 0.15% of the students spent more than what amount of money on textbooks in a semester?
435+3(32)= 531
the histogram below displays the distribution of 50 ages at death due to trauma(accidents and homicides) that were observed in a certain hospital during a week what percentage of deaths were individuals younger than 35?
68%
National longitudinal study of adolescent health based on the table above, the percentage of dating participants, who were not obese is____%
80/438(VERTICAL DIVISION)
Decide if random variable X is binomal or not 1/10 people are left-handed x= number of people who are left-handed out of random sample of 200 individuals without replacement vast pop-independent
Binomial
Height of students at college u= 175 cm std= 6cm sample of 1000 student that the # of students with heights less than 163?
EXCEL norm.dist(163,175,6,1) (100) =23
Bureau of labor stats u=$28.08 std= 1.97 jeronia is social worker with an hourly wage of 31.60 whats her z-score?
EXCEL: =standardize(31.60,28.08,1.97) =1.79
Suppose that P(A)= 0.98. Which of the following is the best interpretation of this statement?
Event A is extremely likely, but in a long sequence of trails, it occasionally will not occur.
Suppose that P(A)= 0.3. Which of the following is the best interpretation of this statement?
Event A will occur less often than not, but it is not extremely unlikely
The faculty senate at a large university wanted to know what proportion of the students though foreign language classes should be required for everyone. True or False? Since the sample is random, it is representative of the population of interest
FALSE
consider the following scatterplot, regression equation, and correlation of midterm and final exam scores for a class of 15 students. which of the following are true statment y=90.6-0.489x, r=-0.602 I. the same number of students scored 100 on the midterm exam as scored 100 on the final exam II. student who scored higher on the midterm exam tended to score higher on the final exam III. the correlation between midterm and final exam scores is negative IV. the standard deviation of the final exam scores is greater than the standard deviation of the midterm exam scores
I and III
suppose that the regression for predicting weight(in pounds) from height(inches) is given by weight=-115+3.6(height) I. a person who is 61 inches tall will weigh 104.6pounds II. for every additional inch of height, the predicted weight will increase, on average, by 3.6pounds III. the correlation between weight and height is negative which of the following statements is correct?
II only
here are two datasets for dataset A, the mean and median are 68. looking at dataset b, notice that all of the observations except the last one are close together. which measure will be affected by this last observation in dataset b
MEAN
the boxplot below show the number of marshmallows in a bag, as estimated by students in two elementary school classes which class has greater variability in students' estimate of the number of marshmallows?
Ms.Apple's class
Number of failures in elementary stats course 0= 0.41 1= 0.15 2= ? 3= 0.05 4= 0.17
P(X=2)= 0.41+0.15+0.05+0.17= 0.78 1-0.78= 0.22 P(X<2)= 0.41+0.15= 0.56 P(X<=2)= 0.41+0.15+0.22= 0.78 P(X>2)= 0.05+0.17= 0.22
Number of visits to Dentists 1= 0.27 2= 0.43 3= 0.18 4= 0.08 5= 0.04
P(x>2)= 0.27 P(x>=3)= 0.18+0.08+0.4= 0.3 P(1<X<=3)= 0.43+0.18= 0.61 P(3<=X<5)= 0.18+0.08= 0.26 P(3<X<5)= 0.08
Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot choose the correct label for the point on the boxplot represented by the question mark:
Q3
which of the tables is the appropriate table of conditional percentages to discover if the region where one lives affects whether or not one has health insurance?
TABLE A
Distribution scores u=22 std=2 do not apply SD deviation rule a)what proportion of students scored at least 29pts of test? b)what is the 42 percentile of score>
a) 1-norm.dist(29,22,2,1) = B) norm.inv(0.42,22,2) =21.596
recent tests closely followed a normal distribution u=22pts std=2pts a) proportion of students scored at least 21pts on test b)what is the 71 percentile of distribution of test scores
a)1-norm.dist(x,u,std,1) b) norm.inv(0.71, mean, std) 71 percentile exam: 23.107
Left handed People 17% people are left handed we select 5 people at random what is the probability? a)there are some lefties(>=1) among the five? b)exactly 3 lefties in group c)at least 4 lefties d) no more than 2 lefties in group e)expectation of lefties f) standard deviation
a)EXCEL: 1-binom.dist(0,5,0.17,1) =0.6061 b)EXCEL: binom.dist(3,5,0.17,0) =0.0338 c)EXCEL 1-binom.dist(3,5,0.17,1) =0.0036 d) EXCEL binom.dist(2,5,0.17,1) =0.9625 e) (0.17)(5)= 0.85 F)divde/5(0.17)(1-0.17)
Large population college student; math anxiety 20% of students have anxiety random sample of 10 students probability of EXACT 2 students have it
binom.dist(2,10,0.20,0) =0.3020
what type of variable is region?
categorical
National Longitudinal Study of Adolescent Health in this example, which of the following would it be appropriate to calculate?
conditional column percentages
the weights(in pounds) and cholesterol levels(in mg/dL) of several individuals were observed. the data are shown in the scatterplot below: the outlier on the graph is likely due to an error in recording the data. which of the following statements is true?
if the outlier were removed, the correlation coefficient(r) would increase
suppose joan has a fair four-sided die with sides that are numbered 1,2,3,and 4 after she rolls it 20 times, how many times does she roll the number 3?
it is impossible to tell
the boxplot below show the real estate values of single-family homes in two neighboring cities(in thousands of dollars) which city has more household?
it is impossible to tell from the boxplot
Left-handed occurs in 12% of Americans male/female males are slightly more likely than female 13% of male 11% female random sample of 80 females and 100 males is chosen x= # of males(out of 100) y=# of females(out of 80) z= total # (males and females together) what is true?
males(x), n=100, p=0.13 mean: 100 x 0.13= 13 Variance: (100)(0.13)(1-0.13) =11.31 Female; n2=80. p2=0.11 mean(80)(0.11)= 8.8 variance: (80)(0.11)(1-0.11) =7.832 need to satify np>=10 np(1-p)>=10 only x can be approximated by normal random variable
Carton of transistors 92% contains no defective 3% contains one defective 3% contains two defective 2% contains three defective calculates mean variance
mean: (0)(0.92)+(1)(0.03)+(2)(0.03)+(3)(0.02) = 0.15 variance: 0.92(0-0.15)^2 + 0.03(1-0.15)^2+ 0.03(2-0.15)^2 + 0.02(3-0.15)^2 = 0.3075
Flower Arrangement(daily) 19= 0.20 20= 0.21 21=0.31 22= 0.14 23= 0.14 mean? varience? standard deviaion?
means: EXCEL =sumproduct(array 1, array2) =20.81 variance: 0.20(19-20.81)^2 + 0.21(20-20.81)^2 + 0.31(21-20.81)^2 + 0.14(22-20.81)^2 + 0.14(23-20.81)^2 =1.6739 standard deviation /varince /1.6739 = 1.2938
in order to obtain a sample of undergraduate students in the United States, a simple random sample of 10 states is selected. from each of the selected states, 10 colleges or universities are chosen at random. finally, from each of these 100 college or universities, a simple random sample of 20 undergraduate students is selected. Thus, the final sample consists of 2,000 undergraduates. this is an example of which type of sampling strategy?
multistage sampling
UC Berkeley Bicycles 12% of registered bicycles stolen each year, random sample of 160 registered bikes x= numbers of bikes stolent
n=160 p=0.12
weights of cockroaches living in a typically colelge dorm are u=80 grams std= 4 grams percentage of cockroaches weighting between 77g and 83g is?
norm.dist(83,80,4,1)-norm.dist(77,80,4,1) (100) =55%
Prescription drug 18%= nausea 41%= decrease sex drive 10%=both probability of just nausea?
p(n)-P(N n D) 0.18-.10=0.8
National longitudinal study of adolescent health calculate the column conditional percentages for participants who ere cohabiting:
perc 2= total perc= 100%(ALWAYS)
a study seeks to answer the question "does vitamin c level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" in this scenario, "level of vitamin C" is what type of variable
quantitative
what type of variable is income?
quantitative
what can we say about the relationship between the correlation r and the slop b of the least-squares line for the same set of data?
r and b have the same sign(+ or -)
in order to study whether there is a relationship between gender and age at marriage, 50 couples were randomly selected and the age of the bride and groom were recorded which of the following would be a meaning display from this study?
side by side boxplots
the boxplots below display annual incomes(in thousands of dollars) of households in two cities which city has greater variability in income?
statstown
the cost of taking your pet aboard the air flight with you in the continental US varies according to the airlines. the five number summary for prices based on a sample of major US airline was min=60, Q1=100, median=110, Q3=125, max=150 which of the following is true about this data?
the lower price is an outlier
an instructor asked for students how much time(to the nearest hour) they spent studying for the midterm. the data are displayed in the followin histogram: what do the numbers on the vertical axis represent
the values of the number of hours studied
the data in the scatterplot below are an individual's weight and the time it takes on a treadmill to raise his or her pulse rate to 140 beats per minute. The 0s correspond to females and the +'s to males which of the following conclusions is more accurate?
there is a negative correlation between time and weight for males and for femalesf
the data in the scatterplot below are an individual's age and the expected life span. the circles correspond to females and te x's to males. which of the following conclusions is most accurate?
there is negative correlation between age and life expectancy for both males and females
suppose that the correlation r between two quantitative variables was found to be r=0. Which of the following is the best interpretation of this correlation value?
there is no linear relationship between the two variables
which city has a greater percentage of homes with real estate values between 45,000 dollars and 85,000 dollars?
tinytown
a researcher wants to determine if preschool attendance is associated with high school graduation for low income student which of the following is the response variable in this study?
whether or not a subject graduates high school
a researcher wants to determine if preschool attendance is associated with high school graduation for low income students which of the following is the response variable in this study?
whether or not a subject graduates high school
Blood type: US and Australia 4% US 1.5% Australia Random sample of US residents(50) and Australians(4) X: # of US(50) with blood type of AB Y: # of Australian(out of 40 w/AB) Z: toal # of individuals(90) w/ AB which is true?
x is binomial random variable with n=50, p=0.04 y is binomial random variable with n=40 p=0.015
Engineering school 55% male 34% between 18-20 24% both Female OR between of 18-20
| 18-20| Not 18-20| total M 0.24 0.31 0.55 F 0.10 0.35 0.45 t 0.34 0.66 1.0 =0.45+0.34-0.10 =0.69
