STAT 200-Masterquiz7 solutions
STAT 200-Masterquiz7 solutions
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Date Created: 11/06/15
1 A birth is selected at random Define events B the baby is a boy and F the mother had the u during her pregnancy The events B and F are A disjoint and independent B disjoint but not independent C independent but not disjoint D neither disjoint nor independent The events are independent but not disjoint ie mutually exclusive since they can both occur y Points Earned 11 Correct Answer C Your Response C 2 For the following statement determine if it is true or false If two events A and B are mutually exclusive they must also be independent A True B False False Just the opposite if mutually exclusive then independent Think of the events being Male and being Female These two events are mutually exclusive since you can only be in one of the events However knowing that you are in event Male automatically disqualifies you from being in event Female so the Pmale is dependent on Pfemale and viceversa g Points Earned 11 Correct Answer B Your Response B 3 According to the Penn State Fact Book University Park approximately 55 of first year students graduate in 4 years this is based on the average of those fulltime firstyear students from 1999 and 2000 who graduated in 4 years and the percentage of firstyear full time undergraduate female students for Fall 2005 is approximately 45 If a freshman student from last fall is chosen at random what is the probability that the student is a female and will graduate in four years A 25 B 100 C 50 The answer is found by taking 55 times 45 which comes to roughly 25 W Points Earned 11 Correct Answer A Your Response A 4 According to the Penn State Fact Book for Enrollment by Ethnicity Fall 2005 University Park in a class of 30 students there would be 17 males and 13 females Let us say that out of these 30 students five are A students three of which are males If a student is chosen at random what is the probability of choosing a male or an A student A 1930 B 17180 C 1115 You are asked to find PM or A PM PA PA and M Drawing a Venn Diagram such as the one found at See Venn helps trememdously in seeing how to solve this problem PM 1730 PA 530 and M and A 330 Substituting these into the equation for PM and A results in 1730 530 330 1930 g Points Earned 11 Correct Answer A Your Response A 5 Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment Five percent of all VCRs manufactured by a large electronics company are defective Three VCRs are randomly selected from the production line of this company The selected VCRs are inspected to determine whether each of them is defective or good A NOT Binomial B Binomial Binomial all conditions are satisfied y Points Earned 11 Correct Answer B Your Response B According to a 2001 study of college students by Harvard University39s School of Public Health 193 of those included in the study abstained from drinking USA TODAY April 3 2002 Suppose that of all current college students in the United States 20 abstain from drinking A random sample of four college students is selected with the following distribution provided from MINITAB Binomial with n 4 and p 02 X P X X 0 04096 1 04096 2 01536 3 00256 4 00016 6 From the table above what is the probability that at least one student BUT no more than three students in this sample abstain from drinking A 05888 B 05632 C 01792 The question asks for at least 1 but no more than 3 meaning either 1 2 or 3 students abstain The answer is found by adding PX1 PX2 PX3 05888 g Points Earned 11 Correct Answer A Your Response A of 31135 1 f 3 1 7 Fill in the blank Ellen is taking 4 courses for the semester She believes that the probability distribution function for X the number of courses for which she will get an A grade is given above What is the expected number of A s she will get EX A s Answer The expected value is found by taking each outcome times its respective probability and then summing these products The expected payoff then is 001 103 204 3015 4005 175 A s g Points Earned 11 Correct Answer 17 5 Your Response 175 r 1 3 4 I1ZJ 1 um 111 an 8 Joan has noticed that the probability distribution for X number of students in line to use the campus ATM machine when she shows up to use it is shown above The variance of X VX 116 What is the standard deviation of X A 108 B 116 C 135 D 220 The standard deviation is simply the square root of the variance square root of 116 is 108 Note that when reporting standard deviation we always use the positive square root V Points Earned 11 Correct Answer A Your Response A 9 What characteristic of a random variable is described by the expected value A Most likely value B Standard deviation C Mean D Maximum value Mean is synonymous with expected value g Points Earned 11 Correct Answer C Your Response C 10 Suppose that a student needs to buy 6 books for her history course The number of books that she will be able to find used is a binomial random variable X with n 6 and p 030 In other words the probability that she will find any given book used is 030 and is independent from one book to the next What is the expected number of used books she will find EX A 30 B 18 C 20 D 60 This is a binomial situation so expected number is found by np or 603 18 W Points Earned 11 Correct Answer B Your Response B 11 Weights of females have approximately a normal distribution with mean 135 lbs and standard deviation 20 lbs Allison weighs 145 lbs What is the zscore for her weight A B C D 10 020 150 050 The zscore is found by observed meanSD 145 135 10 050 a Points Earned 11 Correct Answer D Your Response D 12 The average time taken to complete an exam X follows a normal probability distribution with mean 60 minutes and standard deviation 30 minutes Using Table amp by what time should 67 of the students have finished the exam ie What is the 67th percentile for X A 600 minutes B 779 minutes C 732 minutes D 825 minutes Converting 67 to 06700 and referencing Table A1 we look inside the table for the the zscore that has cumulative probality closest to 06700 This zscore is 044 and we use this to solve for quotobservedquot in the equation zscore observed meanSD Generally this works out to observed SDzscore mean Substituting observed 30044 60 which equals 732 a Points Earned 11 Correct Answer C Your Response C 13 Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches Using Table A1 about what proportion of college women are between 65 and 68 inches tall A B C D 03413 13413 08413 05000 First recognize that the question asks you to find P65 lt X lt 68 and that you need to convert 65 and 68 to zscores by the equation observed meanSD Doing so results in a zscore of zero for 65 and one for 68 From Table A1 P0 lt X lt 1 equals PZ lt 1 PZ lt 0 08413 05000 03413 g Points Earned 11 Correct Answer A Your Response A 14 Keeping in mind that a normal distribution is a model for a continuous variable which one of the following variables cannot possibly have a normal distribution A People39s opinions about a new tax law favor or oppose B Handspans of adult females C Weights of 5yearold male children D Ounces of soda in cans labeled as having 12 ounces People39s opinions are categorical not continuous The other choices represent continuous variables W Points Earned 11 Correct Answer A Your Response A 15 Verbal SAT scores have approximately a normal distribution with mean equal to 500 and standard deviation equal to 100 The 95th percentile of zscores is z 165 What is the 95th percentile of verbal SAT scores A 335 B 600 C 500 D 665 You need to use algebra to solve for quotobservedquot in the equation zscore observed meanSD Generally this works out to observed SDzscore mean Substituting observed 100165 500 which equals 665 V Points Earned 11 Correct Answer D Your Response D 16 Is the given percent a statistic or a parameter Based on the 2000 Census 395 of the California population of residents who are over 5 years old speak languages other than English at home A Parameter B Statistic Since the percent is referring to the California population it is a parameter g Points Earned 11 Correct Answer A Your Response A 17 For the following study decide if the two samples are independent or paired samples In a random sample of 100 students the change in hours of sleep for each student during and after finals week were compared Are the samples of students39 sleep during finals and after finals independent samples or paired samples A Paired samples B Independent samples Readings were taken twice on the same individuals during finals week and after implying paired samples W Points Earned 11 Correct Answer A Your Response A 18 For the following study decide if the two samples are independent or paired samples In a random sample of 100 students 60 women and 40 men the average hours of sleep during finals week were compared Are the samples of men and women independent samples or paired samples A Independent samples B Paired samples Here they are comparing two independent samples a sample from men and another women V Points Earned 11 Correct Answer A Your Response A 19 Suppose we select a random sample of n 100 students and find that the proportion of students who said they believe in love at first sight is 043 Which statement is not necessarily true A phat 043 B There were 43 students in the sample who said they believe in love at first sight C p 043 D Based on the information provided by the sample we cannot determine exactly what proportion of the population would say they believe in love at first sight p 043 is a parameter representing the population proportion which would not necessarily be known just from the data given W Points Earned 11 Correct Answer C Your Response C 20 Which one of the following statements is false A The standard error of a sample statistic measures roughly the average difference between the values of the statistic and the population parameter B Assuming a fixed value of s sample standard deviation the standard error of the mean decreases as the sample size increases C The standard error of a sample proportion decreases as the sample size increases D The standard error measures the variability of a population parameter The standard error measures the variability of a sample statistic not a population parameter g Points Earned 11 Correct Answer D Your Response D 21 Based on the 2000 Census the proportion of the California population aged 15 years old or older who are married is p 0524 Suppose n 1000 persons are to be sampled from this population and the sample proportion of married persons phat is to be calculated What is the standard deviation of the sampling distribution of phat A 02494 B 00158 C 05240 D 00166 The standard error or standard deviation of the sampling distribution is found by taking the square root of 052404761000 00158 g Points Earned 11 Correct Answer B Your Response B 22 Based on the 2000 Census 318 of grandparents in California are the primary caregivers for their grandchildren Suppose n 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers p hat is to be calculated What is the standard deviation of the sampling distribution of phat A 02169 B 00002 C 00147 D 03180 The standard error or standard deviation of the sampling distribution is found by taking the square root of 03180682 1000 00147 W Points Earned 11 Correct Answer C Your Response C 23 Suppose on a highway with a speed limit of 65 mph the speed of cars are independent and normally distributed with an average speed 65 mph and standard deviation 5 mph What is the expected value of the sample mean speed in a random sample of n 100 cars A 13 mph B 65 mph C 65 mph D 065 mph The expected value of a sample mean would equal that of the population mean 65 mph y Points Earned 11 Correct Answer B Your Response B 24 For which of the following situations would the Rules for Sample Means not apply A A random sample of size 20 is drawn from a skewed population B A random sample of size 20 is drawn from a bellshaped population C A random sample of size 50 is drawn from a bellshaped population D A random sample of size 50 is drawn from a skewed population For sample sizes of 30 or more the Central Limit Theorem states that even for a skewed population the sample mean distribution will approximated a normal distribution and if the population is bellshaped then so to will the distribution of the sample means regardless of sample size Thus the response that does not follow the Rules is the one of sample size of 20 from a skewed distribution V Points Earned 11 Correct Answer A Your Response A 25 Use Table A1 Items produced by a certain process are supposed to weigh 90 grams However the process is such that there is variability in the items produced and they do not all weigh exactly 90 grams The distribution of weights is normal with a mean of 89 grams and a standard deviation of 1 gram If we have a random sample of 4 of these items what is the probability that their average weight exceeds 90 grams A 05987 B 04013 C 00228 D 09772 You are asked to find PXbar gt 90 First you need to convert to a zscore by obs meanSE 90 891sqrt 4 105 20 This translates to PZ gt 20 and from Table A1 this equals 1 09772 00228 W Points Earned 11 Correct Answer C Your Response C 26 Did you work on this quiz by yourself or with a partners A By myself B With partners W Points Earned 00 Correct Answer Your Response A
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