1) The table lists the smoking habits of a group of college students. Answer: 0.218


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1 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Nonsmoker Regular Smoker Heavy Smoker Total Man Woman Total 22 2 If a student is chosen at random, find the probability of getting someone who is a regular or heavy smoker. Round your answer to three decimal places. Answer: ) The distribution of Master's degrees conferred by a university is listed in the table. (assume that a student majors in only one subject) Major Frequency Mathematics 20 English 208 Engineering 86 Business 6 Education 222 What is the probability that a randomly selected student with a Master's degree majored in English or Mathematics? Round your answer to three decimal places. Answer: 0.5 ) In the game of craps, two dice are tossed and the up faces are totaled. Is the event getting a total of 9 and one of the dice showing a 6 mutually exclusive? Answer Yes or No. Answer: No ) The table lists the smoking habits of a group of college students. Sex Nonsmoker Regular Smoker Heavy Smoker Total Man Woman Total If a student is chosen at random, find the probability of getting someone who is a woman or a heavy smoker. Round your answer to three decimal places. Answer: ) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a seven or a nine or a heart or a diamond. Answer: 0.5 6) You are dealt one card from a 52card deck. Find the probability that you are not dealt a. Answer: 2
2 ) A game has three outcomes. The probability of a win is 0., the probability of tie is 0.5, and the probability of a loss is 0.. What is the probability of not winning in a single play of the game. Answer: 0.6 8) A human gene carries a certain disease from the mother to the child with a probability rate of %. That is, there is a % chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. Answer: ) A human gene carries a certain disease from the mother to the child with a probability rate of 9%. That is, there is a 9% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has five children. Assume that the infections of the five children are independent of one another. Find the probability that at least one of the children get the disease from their mother. Answer: ) In how many ways can a committee of three men and four women be formed from a group of 0 men and 0 women? Answer: ) How many distinct arrangements can be formed from all the letters of "statistics"? Answer: 50,00 2) Given the sets of digits {,,, 6, 8}, how many different numbers between 0,000 and 80,000 can be written using these digits if repetition of digits is allowed? Answer: 250 ) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last. Answer: 20; 2; 0 ) From 8 names on a ballot, a committee of will be elected to attend a political national convention. How many different committees are possible? Answer: 56 5) The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. x P(x) Answer: mean:.8; standard deviation:.0 2
3 6) The probability that a tennis set will go to a tiebreaker is %. What is the probability that two of three sets will go to tiebreakers? Answer: 0.02 ) The probability that a house in an urban area will be burglarized is 2%. If 29 houses are randomly selected, what is the probability that none of the houses will be burglarized? Answer: ) An airline has a policy of booking as many as 50 persons on a plane that seats 0. Past studies indicate that only 85% of booked passengers show up for their flight. Find the probability that if the airline books 50 persons for a 0seat plane, not enough seats will be available. Answer: ) A test consists of 690 true or false questions. If the student guesses on each question, what is the mean number of correct answers? Answer: 5 20) The probability that an individual is lefthanded is 0.. In a class of 0 students, what is the mean and standard deviation of the number of lefthanders in the class? Answer: mean: 9.; standard deviation: ) Find the area under the standard normal curve between z = 0 and z =. Answer: ) Find the sum of the areas under the standard normal curve to the left of z = .25 and to the right of z =.25. Answer: ) For a standard normal curve, find the zscore that separates the bottom 0% from the top 0%. Answer: 0.5 2) IQ test scores are normally distributed with a mean of 02 and a standard deviation of. An individual's IQ score is found to be 0. Find the zscore corresponding to this value. Answer: 0.8 Determine the area under the standard normal curve that lies a) above and b) below the given Zscore. 25) z = 0. Answer: 5.98%, 6.02% Suppose that prices of a certain model of new homes are normally distributed with a mean of $50,000. Find the percentage of buyers who paid: 26) between $50,000 and $55,00 if the standard deviation is $00. Answer: 9.85% 2) A physical fitness association is including the mile run in its secondaryschool fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 50 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 2 seconds. Answer:.00
4 28) Suppose a brewery has a filling machine that fills 2 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 2. ounces and a standard deviation of 0.0 ounce. Find the probability that the bottle contains between 2.2 and 2.0 ounces. Answer: ) Professor Whata Guy surveyed of his Introduction to Statistics class of 20 students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion, p? Answer: 0.6 0) Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift 5% of all welds done will be substandard. If Smith checks 00 of the 500 welds completed that shift, what is the probability that he will find less than 20 substandard welds? Answer: ) A survey of 500 nonfatal accidents showed that 222 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone. Answer: (0.8, 0.50) 2) An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 6% would like more discussion about the family's financial situation, % would like to talk about school, and 0% would like to talk about religion. These and other percentages were based on a national sampling of 5 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. Answer:. ±.05 ) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. Answer:.5625 ±.029 ) Construct a 90% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 5 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.8. Answer: (2.5,.2) 5) How much money does the average professional football fan spend on food at a single football game? That question was posed to 0 randomly selected football fans. The sampled results show that sample mean and standard deviation were $8.00 and $.0, respectively. Use this information to create a 95% confidence interval for the mean. Answer: 8 ± 2.262(.0/ 0) 6) Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 8.5 with a standard deviation of 0.2. Answer: (.29, 85.)
5 ) A random sample of 0 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. $.60 $.50 $2.80 $6.0 $2.60 $5.20 $6.5 $.25 $8.00 $.00 Find the 95% confidence interval for the true mean. Answer: ($.9, $6.0) 8) The grade point averages for 0 randomly selected high school students are listed below. Assume the grade point averages are normally distributed Find a 98% confidence interval for the true mean. Answer: (.55,.5) 9) Suppose you are using = 0.05 to test the claim that µ 2 using a Pvalue. You are given the sample statistics n = 5, x =., and = 2.. Find the Pvalue. Answer: ) Given H0: µ = 25, H: µ 25, and P = Do you reject or fail to reject H0 at the 0.0 level of significance? Answer: fail to reject H0 ) Given H0: µ 8, H: µ < 8, and P = Do you reject or fail to reject H0 at the 0.05 level of significance? Answer: fail to reject H0 2) A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5. A random sample of 0 teachers provided the data below. At = 0.05, test the district's claim using Pvalues Answer: Pvalue = , P <, reject H0; There is sufficient evidence to support the school district's claim. 5
6 Provide an appropriate response. ) Construct a scatter plot for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. x y Answer: There appears to be no linear correlation. ) Calculate the correlation coefficient, r, for the data below. x y Answer: ) The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Calculate the correlation coefficient r. Gestation, x Life span, y Answer: ) In order for applicants to work for the foreignservice department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. Calculate the correlation coefficient, r. Number of years, x Grades on test, y Answer: 0.9 ) Given a sample with r = 0.5, n = 20, and = 0.0, determine the standardized test statistic t necessary to test the claim = 0. Round answers to three decimal places. Answer:.29 6
7 8) Given a sample with r = 0.65, n = 22, and = 0.02, determine the standardized test statistic t necessary to test the claim = 0. Round answers to three decimal places. Answer: ) For the data below, test the significance of the correlation coefficient using = 0.0 and the claim = 0. x y Answer: critical value t0 = ±.860; standardized test statistic t 0.296; fail to reject H0; There is not sufficient evidence to conclude that a significant correlation exists. 50) Given a sample with r = 0.5, n = 20, and = 0.0, determine the critical values t0 necessary to test the claim = 0. Answer: ± ) Find the equation of the regression line for the given data. x y Answer: y = 2.09x ) The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the equation of the regression line for the given data. Gestation, x Life span, y Answer: y =.52x ) A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. Miles traveled, x Sales, y ) 55) Answer: y =.529x +.96 Given the equation of a regression line is y =.5x  5., what is the best predicted value for y given x = .2? Assume that the variables x and y have a significant correlation. Answer: 9.6 Given the equation of a regression line is y = .5x., what is the best predicted value for y given x = 9.5? Assume that the variables x and y have a significant correlation. Answer: 6.5
8 use alpha.05 the given data to find the best predicted value of the response variable. 56) The regression equation relating dexterity scores (x) and productivity scores (y) for the employees of a company is y = x. Ten pairs of data were used to obtain the equation. The same data yield r = and y = 56.. What is the best predicted productivity score for a person whose dexterity score is 2? 5) 58) Answer: Six pairs of data yield r = 0. and the regression equation y = 5x + 2. Also, y = 8.. What is the best predicted value of y for x = 5? Answer: 8. Nine pairs of data yield r = 0.86 and the regression equation y = x. Also, y = 6.. What is the best predicted value of y for x = 50? Answer:
9 Answer Key Testname: FINAL_EXAM_REVIEW ) ) 0.5 ) No ) ) 0.5 6) 2 ) 0.6 8) ) ) ) 50,00 2) 250 ) 20; 2; 0 ) 56 5) mean:.8; standard deviation:.0 6) 0.02 ) ) ) 5 20) mean: 9.; standard deviation: ) ) ) 0.5 2) ) 5.98%, 6.02% 26) 9.85% 2).00 28) ) 0.6 0) ) (0.8, 0.50) 2). ±.05 ).5625 ±.029 ) (2.5,.2) 5) 8 ± 2.262(.0/ 0) 6) (.29, 85.) ) ($.9, $6.0) 8) (.55,.5) 9) ) fail to reject H0 ) fail to reject H0 2) Pvalue = , P <, reject H0; There is sufficient evidence to support the school district's claim. 9
10 Answer Key Testname: FINAL_EXAM_REVIEW ) There appears to be no linear correlation. ) ) ) 0.9 ).29 8) ) critical value t0 = ±.860; standardized test statistic t 0.296; fail to reject H0; There is not sufficient evidence to conclude that a significant correlation exists. 50) ± ) y = 2.09x ) y =.52x ) y =.529x ) ) ) ) 8. 58)
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