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##### MATH 533 Final Exam

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Question;MATH533;? Final Exam Worksheet;Given;the following sample of 10 high temperatures from March: 55, 60, 57, 43, 59, 66, 72, 65, 59, 47.;Determine the mean.Determine;the median.Determine;the mode.Describe;the shape of the distribution.Determine;Q1, Q2, Q3 and IQR.;The;contingency table shows classification of students in a Statistics class.;From NJ;From PA;GPA at least 3.0;15;5;20;GPA below 3.0;45;35;80;60;40;100;If;a student is selected at random, what is the probability that he/she is from NJ?If;a student is selected at random, what is the probability that he/she has a GPA;below 3.0?If;we know that the student is from PA, what is the probability that he/she has a;GPA of at least 3.0?If;a student is selected at random, what is the probability that he/she is from NJ;and has a GPA below 3.0.If;a student is selected at random, what is the probability that he/she from PA and;has GPA of at least 3.0.;Your;friend is applying for 4 jobs. The;hourly pay rate for the 4 jobs are, \$8, \$12, \$15, \$20. The probability distribution below shows the;probability of getting each of these jobs;Job Pay;Rate, X;Probability;P(X);8;.30;12;.20;15;.40;20;.10;What;is the probability that your friend will get a job paying at least \$15/hour?What;is the expected pay rate for your friend?;It;is known that 31% of cars are considered gas hogs (i.e. they give less than 15;mpg). If we select 20 cars at random:What;is the probability that exactly 4 will be gas hogs?What;is the probability the at least 4 but not more than 7 will be gas hogs?How;many cars are most likely to be gas hogs?You;ask all 200 students at school how much money they have in their pockets. The amount ranges from \$0 to \$130. You determine the mean to be \$56.40 with;standard deviation of \$8.40. You believe;that the amount is normally distributed.If;you pick a person at random, what is the probability that he/she has at least;\$45?What;percentage of the students will have between \$40 and \$50 in their pockets.If;you pick a person at random, what is the probability that he/she has either;less than \$30 or more than \$70.Approximately;how many people in the class do you expect to have at least \$65?We;want to identify the students with top 10.5% amounts as ?rich?. What is the minimum dollar amount the;students in this group would need in their pockets.Assume;that on the third exam in a calculus course, the average score over the years;has been 72 with a standard deviation 12.;You are currently taking the course and there are 25 students in the;class?;What is the probability that the;mean score for your class will be greater than 75?;What is the probability that the;mean score for your class will be between 68 and 70?;A;sample of 25 days in summer yields an average high temperature of 80 with a;standard deviation of 12.Give;a point estimate of the true mean of the high temperature.Find;a 99% confidence interval for the average high temperature for the summer.How;big a sample do we need if we want to be 90% confident of being within 7;degrees of the population mean?A;sample of 100 exams yielded an average grade of 82 and standard deviation of;14. Find a 95% confidence interval for;the average exam grade.Heights;of aliens from Mars are known to be normally distributed with a population;standard deviation of 9 inches. How big;a sample do we need to take if we want be 95% confident that our error will not;exceed 3 inches?;Preliminary;studies have shown that 20% of the voters might be willing to vote for Sran for;President. Construct;a 90% confidence interval for the proportion of voters who would be willing to;support Sran.Before;entering the race, Sran would like to conduct a poll to check his level of;support. How big should be the sample be;if he wants to be 95% sure that the error is no more than 2%?The;average weight of men joining a gym has historically been 170 pounds with a;standard deviation of 27. The owner;feels that the average weight has now decreased to less than 165 pounds. To support his claim, the owner conducts a;sample of 25 men and finds their average to be 153. He would like to use a significance level of;.05 to test his claim.State;the null hypothesis.State;the alternate hypothesis.Will;you use z or t distribution for this problem?Is;this a two-tail test or a one-tail test?;Draw a normal curve representing the problem.Determine;the critical value.Determine;the rejection region.Calculate;the test statistic.Would;you accept or reject the owner?s claim?;Explain.The;average score on a certain college entrance test has been known to be 240. The dean of a university feels that this has;changed. He conducts a sample of 25;students to test his claim. The sample;yields an average of 232 with a standard deviation of 25. He would like to use;a significance level of.10.State;the null hypothesis.State;the alternate hypothesis.Will;you use z or t distribution for this problem?Is;this a two-tail test or a one-tail test?;Draw a normal curve representing the problem.Determine;the critical value.Determine;the rejection region.Calculate;the test statistic.Would;you accept or reject the dean?s claim?A presidential candidate states that she;currently has exactly 30% of the vote. A;newspaper thinks that this number is inaccurate. So it conducts a sample 500 voters and finds 175;people support the candidate. The;newspaper would like to test its claim using.05 significance level.State;the null hypothesis.State;the alternate hypothesis.Will;you use z or t distribution for this problem?Is;this a two-tail test or a one-tail test?;Draw a normal curve representing the problem.Determine;the critical value.Determine;the rejection region.Calculate;the test statistic.Would;you accept or reject the newspaper?s claim?

Paper#60773 | Written in 18-Jul-2015

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