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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#60812 | Written in 18-Jul-2015

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