Math 1530 Practice Test 2 Chapter 5 Probability 1 A group of 5 students has to select 3 of them to attend a student government conference Suppose the students are Andy Bill Charlene Danielle and Edward A B C D E a Write the sample space S for all possible three person choices A B C is one to attend the conference b If F is the event that Bill and Danielle will be two of those selected list the outcomes in F If each outcome in S is equally likely find the probability that c Andy is one of those chosen d either Bill or Edward is chosen e at least one girl Charlene Danielle is chosen 2 The following table gives data on the ages of students in several statistics classes Age Range frequency 17 19 28 20 22 33 23 25 27 26 29 7 30 33 5 Total 100 a Are the events over 25 years old and between 30 and 33 years old mutually exclusive Find the probability that a randomly selected student b is either a teenager or between 23 and 25 years old c is less than 30 years old d is in his her twenties 3 A check of dorm rooms on a large college campus revealed that 38 had refrigerators 52 had TV s and 21 had both a TV and a refrigerator Draw and label a Venn diagram to reflect this information don t forget to convert the percents to decimals Then answer the following questions What s the probability that a randomly selected dorm room has a a TV but no refrigerator b a TV or a refrigerator but not both c neither a TV nor a refrigerator d a TV given that it has a refrigerator 4 A poll on a college campus classified respondents by gender and political party as shown in the table below Find the following probabilities a P M b P M and D c P F or I d P M D e Are M and D independent events Justify your answer D emocrat R epublican I ndependent M ale 36 45 24 105 F emale 48 33 16 97 Chapter 6 The Normal Distribution 5 If the scores on a test are normally distributed with a mean of 50 and a standard deviation of 5 what percent of all scores will be between 40 and 60 according to the empirical rule Find the percentage of data in the indicated regions under the standard normal curve 6 less than 1 4 7 between 1 and 1 5 8 greater than 2 2 9 What property of the Normal distribution guarantees that the area to the right of z 1 35 is the same as the area to the left of z 1 35 10 A certain skills test has normally distributed scores with mean 60 and standard deviation 4 a What percent of scores will be between 58 and 63 b What percent of scores will be less than 53 c If the bottom 20 of all scores fail the test what is the cutoff score for a passing grade d If the top 10 of scores receive a special certificate what is the minimum score needed to get a certificate Chapter 7 Sampling Distributions Sample Distribution Model for Sample Proportions In each problem 11 13 assume that the samples are random and less than 10 of the population thus the elements of the sample are considered independent Check the conditions for np and nq to be sure a Normal model is appropriate In each problem give the mean for the model and the standard deviation for the model Then draw the appropriate Normal curve shade the appropriate area and answer the given question 11 The proportion of voters favoring annexation in a certain area is 57 Samples of size 150 are taken What is the probability that the proportion of voters favoring annexation in a random sample of 150 voters is between 55 and 60 12 The proportion of voters favoring a city manager style of government in a certain city is 38 Samples of size 90 are taken What is the probability that the proportion of voters preferring a city manager style of government in a sample of 90 voters will be less than 32 13 In a particular manufacturing process the percentage of defective products is 3 6 Samples of size 400 are taken What is the probability that a sample of size 400 will have more than 5 5 defectives Sample Distribution Model for Sample Means In each problem 14 16 assume that the samples are random and less than 10 of the population Check to be sure that the sample size is large enough to justify a Normal model In each case give the mean for the model and the standard deviation for the model After drawing the appropriate Normal curve and shading the appropriate area answer the given question 14 The weights of a certain type of ball bearing are normally distributed with a mean of 72 grams and a standard deviation of 6 4 grams Samples of size 16 are taken What is the probability that a sample of 16 ball bearings will have a mean weight less than 70 grams 15 The lengths of adult fish in a certain species of bass have an approximately normal distribution with a mean of 11 in and a standard deviation of 1 6 in Random samples of size 20 are taken What is the probability that in a sample of 20 adult bass the mean length will be between 11 5 and 11 8 inches 16 The number of siblings for Americans has a highly right skewed distribution with a mean of 1 7 and a standard deviation of 0 6 Samples of size 50 are taken What is the probability that in a sample of size 50 the mean number of siblings will be greater than 1 9 17 Scores on an aptitude test are normally distributed with a mean of 280 and a standard deviation of 30 Determine the percentage of samples of size 4 that have a mean score within 21 points of the population mean 280 18 One barge from Inland Waterways Inc can carry a load of 5516 8 lb Records of past trips show that the weight of cans that it carries have a mean of 82 lb and a standard deviation of 16 lb For samples of size 64 find the mean and standard deviation of the distribution of the sample mean 19 The mean height for a population is 65 inches and the standard deviation is 3 inches Let denote the mean height for a simple random sample of people from the population True or False The standard deviation of for samples of size 30 is greater than the standard deviation of for samples of size 20