Statistics Questions

a b 1 Which of the following expressions are equivalent to 5 None of the above 5 4 5 5 Part B Consider the following equation 13 13 13 67 67 13 67 Here and y 1 1 1 5 5 5

Solve 3 7 11 AM 1 BV 2 6 D D x 2

Solve the following expression Select all that apply t 3 15 At 3 45 B42 C 45 D9 3

17 Hint s 1 1 Solve for x 3x 4 9z 3 A B D 3 C3 None of the above HIDENT

29 Graph the solution to the following inequality 38 k 5 2k 40 39 38 37 36 ECT 35 34 O UNDO 33 REDO 32 RESET 31 REMOV 34

What is the solution to the inequality 3 2x 1 4z 2 1 B H 1212 2 212 2

Simplify the Radical 215 15 A B 4x 15 6x 0 10 615 10 D 60

24 Divide the following expression and write the result as a whole number 7 90 x 10 2 1 0 x 10 5

23 What is the solution to 3x 30 10 2x 5x 2 6 2 9 2 18

7 Express this product in scientific notation 11 10 12 10 A 13 2 x 1025 B 132 x 10 5 1 32 x 10 3 1 32 x 10 5 SHOW HINT

2 Select an expression that is equivalent to 38 A 34 B36 31 D 33

Solve the following linear equation for x 5x 2 x 9 3x 10

ABC Corp transfers an instrument to Wilson Inc An employee at ABC Corp alters the amount on the note to 24 200 from 12 000 before selling it to Wilson Inc Wilson Inc then transfers the instrument to Blowtorch Inc Blowtorch Inc accepts the instrument but later discovers that the instrument has been altered Blowtorch approaches Wilson Inc and asks them to return the money It is then discovered that an employee at ABC Corp made the alteration in the instrument and kept the extra amount paid by Wilson Inc for himself Since the difference between the altered amount and the original amount is large the employee says he cannot pay the amount Which of the following is true in this situation a Wilson Inc cannot claim the extra money from ABC Corp because it has already transferred the instrument to Blowtorch Inc O b ABC Corp is responsible for its employee s actions and is liable because its employee cannot pay c Blowtorch Inc cannot claim the money since it accepted the instrument in the first place d ABC Corp is not liable regardless of the financial situation of its employee because the employee kept the additional amount for himself Check My Work 1 remaining

Suppose that the probability that a passenger will miss a flight is 0 0948 Airlines do not like flights with empty seats but it is also not desirable to have overbooked flights because passengers must be bumped from the flight Suppose that an airplane has a seating capacity of 52 passengers a If 54 tickets are sold what is the probability that 53 or 54 passengers show up for the flight resulting in an overbooked flight b Suppose that 58 tickets are sold What is the probability that a passenger will have to be bumped c For a plane with seating capacity of 250 passengers what is the largest number of tickets that can be sold to keep the probability of a passenger being bumped below 1 a The probability of an overbooked flight is Round to four decimal places as needed

Suppose that a recent poll found that 42 of adults believe that the overall state of moral values is poor Complete parts a through c a For 300 randomly selected adults compute the mean and standard deviation of the random variable X the number of adults who believe that the overall state of moral values is poor The mean of X is Round to the nearest whole number as needed

According to flightstats com American Airlines flights from Dallas to Chicago are on time 80 of the time Suppose 20 flights are randomly selected and the number of on time flights is recorded a Explain why this is a binomial experiment b Determine the values of n and p c Find and interpret the probability that exactly 12 flights are on time d Find and interpret the probability that fewer than 12 flights are on time e Find and interpret the probability that at least 12 flights are on time f Find and interpret the probability that between 10 and 12 flights inclusive are on time a Identify the statements that explain why this is a binomial experiment Select all that apply A The trials are independent B The experiment is performed until a desired number of successes are reached C The probability of success is different for each trial of the experiment D The experiment is performed a fixed number of times E There are two mutually exclusive outcomes success or failure F There are three mutually exclusive possible outcomes arriving on time arriving early and arriving late G The probability of success is the same for each trial of the experiment H Each trial depends on the previous trial

According to a study done by Nick Wilson of Otago University Wellington the probability a randomly selected individual will not cover his or her mouth when sneezing is 0 267 Suppose you sit on a bench in a mall and observe people s habits as they sneeze Complete parts a through c a Using the binomial distribution what is the probability that among 10 randomly observed individuals exactly 5 do not cover their mouth when sneezing The probability is nimel plocos as needed

A market researcher is studying the spending habits of people across age groups The amount of money spent by each individual is classified by spending category Dining out Shopping or Electr nics Factor A and generation Gen X Gen Y Gen Z or Baby Boomers Factor B An incomplete ANOVA table is shown below Source of Variation Rows Factor B Columns Factor A Error Total Multiple Choice O SS O 46 869 1 321 831 df 35 At the 5 significance level the conclusion of the hypothesis test for factor A is MS 79 930 reject the null hypothesis we cannot conclude the average amount spent differs by spending category do not reject the null hypothesis we cannot conclude the average amount spent differs by spending category do not reject the null hypothesis we can conclude the average amount spent differs by spending category reject the null hypothesis we can conclude the average amount spent differs by spending category

5 The number of customers entering a store each day over the course of 30 days is summarized by the frequency histogram below Frequency 12 10 8 2 0 0 30 Answer 60 90 Number of Customers 120 What percentage of the 30 days had at least 90 customers enter the store Enter your answer as a decimal Previous Answer 0 1667 150

below Academic Subject Biology English History Mathematics What percentage of students selected mathematics Enter your answer as a decimal and round to two decimal places Answer Frequency 3 8 4 5 Previous Answer 25 Return to overview

9 The number of responses to a survey are shown in the Pareto chart The survey asked 985 adults how they would grade the quality of their public schools Each person gave one response Find each probability a Randomly selecting a person from the sample who did not give the public schools an A b Randomly selecting a person from the sample who gave the public schools a grade better than a D c Randomly selecting a person from the sample who gave the public schools a D or an F d Randomly selecting a person from the sample who gave the public schools an A or B a The probability that a randomly selected person did not give the public schools an A is Round to three decimal places as needed b The probability that a randomly selected person gave the public schools a grade better than a D is Round to three decimal places as needed c The probability that a randomly selected person gave the public schools a D or an F is Round to three decimal places as needed d The probability that a randomly selected person gave the public schools an A or B is Round to three decimal places as needed Number responding 400 300 200 100 301 286 251 99 48 0 CDBFA Response Q Q

1 The personnel department of a large corporation wants to estimate the family dental expenses of its employees A random sample of 12 employees reveals the following family dental expenses for the preceding year 15 17 18 13 14 16 17 14 21 25 19 16 Set up a 99 confidence interval estimate of the mean family dental expenses for all employees Critical Values Formula Mean Standard Dev C I E

The graph of the discrete probability to the right represents the number of live births by a mother 40 to 43 years old who had a live birth in 2015 Complete parts a through d below Probability 0 30 0 25 0 20 0 15 0 10 0 05 0 00 0 CL 0 233 0 261 2 0 167 0 109 0 099 0 036 0 041 0 054 4 5 6 Number of Live Births 7 8 a What is the probability that a randomly selected 40 to 43 year old mother who had a live birth in 2015 has had her fourth live birth in that year Type an integer or a decimal b What is the probability that a randomly selected 40 to 43 year old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year Type an integer or a decimal c What is the probability that a randomly selected 40 to 43 year old mother who had a live birth in 2015 has had he sixth or more live birth in that year Type an integer or a decimal d If a 40 to 43 year old mother who had a live birth in 2015 is randomly selected how many live births would you expect the mother to have had Round to one decimal place as needed

K right the random variable represents the number of marriages an individual aged 15 years or older has been involved in Complete parts a through f below Graph the probability distribution Choose the correct graph below O A 0 6 0 5 0 4 0 3 0 2 0 1 04 0 1 2 3 4 5 Number of Marriages Q Q OB The distribution 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 Number of Marriages Describe the shape of the distribution Q OC and is c Compute and interpret the mean of the random variable X Hx marriages Type an integer or a decimal Do not round Which of the following interpretations of the mean is correct A 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 Number of Marriages Q D 0 61 0 5 0 4 0 3 0 2 0 1 0 X 0 1 2 3 4 5 P X 0 272 0 585 0 112 0 026 0 004 0 001 0 1 2 3 4 5 Number of Marriages OA If many randomly selected individuals 40 to 49 years of age were surveyed the sample mean number of marriages should be close to the mean of the random variable OB If any number of individuals aged 15 year or older were surveyed the sample mean number of marriages should be close to the mean of the random variable OC If many individuals aged 15 year or older were surveyed the sample mean number of marriages should be close to the mean of the random variable OD If many randomly selected individuals aged 15 years or older were surveyed the observed number of marriages will be equal to the mean number of marriages for most individuals OE If many randomly selected individuals aged 15 years or older were surveyed the observed number of marriages will be less than the mean number of marriages for most individuals d Compute the standard deviation of the random variable X x marriages Round to one decimal place as needed e What is the probability that a randomly selected individual 15 years or older was involved in two marriages Type an integer or a decimal Do not round f What is the probability that a randomly selected individual 15 years or older was involved in at least two marriages

Q6 School A has mean grade of 80 on an entrance exam with s 5 School B has a mean grade of 70 with s 10 The scores in each school are normally distributed What percentage of students in school B do better than the average student in school A ANSWER 16

In the probability distribution to the right the random variable X represents the number of marriages an individual aged 15 years or older has been involved in Complete parts a through f below a Verify that this is a discrete probability distribution This is a discrete probability distribution because and the of the probabilities is Type whole numbers Use ascending order b Draw a graph of the probability distribution Describe the shape of the distribution Graph the probability distribution Choose the correct graph below OA 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 Number of Marriages Q Q The distribution 5 OB 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 Number of Marriages Describe the shape of the distribution EEXCE and is C c Compute and interpret the mean of the random variable X Hx marriages Type an integer or a decimal Do not round Which of the following interpretations of the mean is correct 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 Number of Marriages Q OD X 0 1 2 3 4 5 between and inclusive A P x O 0 272 0 585 0 112 0 026 0 004 0 001 0 6 0 5 0 4 0 3 0 24 0 1 0 0 1 2 3 4 5 Number of Marriages OA If many randomly selected individuals 40 to 49 years of age were surveyed the sample mean number of marriages should be close to the mean of the random variable OB If any number of individuals aged 15 year or older were surveyed the sample mean number of marriages should be close to the mean of the random variable OC If many individuals aged 15 year or older were surveyed the sample mean number of marriages should be close to the mean of the random variable OD If many randomly selected individuals aged 15 years or older were surveyed the observed number of marriages will be equal to the mean number of marriages for most individuals

The following data represent the number of otholes on 35 randomly selected 1 mile tretches of highway around a particular city Complete parts a through g below Number of Potholes O 3 6 2 7 1 2 3 1 4 1 7 1 1 3 4 5 2 1 5 5 2 3 1 1 6 4 3 7 1 3 1 2 4 6 1 Round to the nearest integer as needed d Using the results from part b what percentage of the stretches of highway have 5 or more potholes Round to the nearest integer as needed e Construct a frequency histogram of the data Choose the correct answer below OA Frequency NO OC 01 Relative Frequency Frequency wa CON O A 12 Potholes Relative Frequency 1234567 Number of Potholes Potholes O C 1234567 Number of Potholes 0 4 0 3 Potholes 0 2 0 1 0 Potholes Q 1234567 Number of Potholes 0 4 0 3 0 2 0 1 0 Q Q f Construct a relative frequency histogram of the data Choose the correct answer below 1234567 Number of Potholes O Skewed right O Skewed left Uniform SOU B Q Frequency 12 O D Frequency Potholes 1234567 Number of Potholes Relative Frequency OB Potholes 1234567 Number of Potholes Relative Frequency 0 4 0 31 0 2 0 1 Potholes O D Q 01234567 Potholes ON 0 47 0 3 Number of Potholes 0 2 0 1 ON 01234567 Number of Potholes ON g Describe the shape of the distribution Choose the correct answer below

The following data represent the number of potholes on 35 randomly selected 1 mile stretches of highway around a particular city Complete parts a through g below Number of Potholes 4 3 1 5 1 3 2 1 1 6 5 4 5 3 2 7 1 4 1 7 1 1 3 1 2 4 6 1 3 6 2 7 1 2 3 This question 1 point s possible a Construct a frequency distribution of the data Frequency Potholes 1 2 3 4 5 6 7 b Construct a relative frequency distribution of the data Potholes Relative Frequency 1 2 3 4 5 6 7 Round to two decimal places as needed c Using the results from part b what percentage of the stretches of highway have 3 potholes Round to the nearest integer as needed d Using the results from part b what percentage of the stretches of highway have 5 or more potholes Round to the nearest integer as needed OA e Construct a frequency histogram of the data Choose the correct answer below 29 O C Frequency o agin Submit quiz Potholes 12 1234567 Number of Potholes Potholes OB Frequency 127 Potholes O D uency 0 1234567 Number of Potholes MUTT Potholes 6 OO o o

Determine whether the random variable is discrete or continuous In each case state the possible values of the random variable a The number of light bulbs that burn out in the next week in a room with 10 bulbs b The time it takes for a light bulb to burn out a Is the number of light bulbs that burn out in the next week in a room with 10 bulbs discrete or continuous OA The random variable is discrete The possible values are 0 x 10 OB The random variable is continuous The possible values are 0 x 10 OC The random variable is continuous The possible values are x 0 1 2 10 OD The random variable is discrete The possible values are x 0 1 2 10 b Is the time it takes for a light bulb to burn out discrete or continuous OA The random variable is continuous The possible values are t 1 2 3 OB The random variable is continuous The possible values are t 0 OC The random variable is discrete The possible values are t 0 O D The random variable is discrete The possible values are t 1 2 3

What are the two requirements for a discrete probability distribution Choose the correct answer below Select all that apply A OSP x 1 B 0 P x 1 C P x 0 D P x 1

61 randomly selected students were asked the number of pairs of shoes they have Let X represent the number of pairs of shoes The results are as follows of Pairs of Shoes 4 5 6 7 8 9 10 Frequency 7 8 12 7 11 10 6 Round all your answers to 4 decimal places where possible The mean is 7 The median is 7 The sample standard deviation is 1 8797 The first quartile is The third quartile is 9 q What percent of the respondents haun

Q7 A frequency distribution of temperatures in Celsius C is presented below Calculate the mean mode and variance for these data Temperature Range 30 39 20 29 10 19 00 09 10 1 20 11 f 9 12 23 30 15 5 1 30 21 ANSWER mean 9 34 mode 4 5 or an interval of 0 9 variance 184 82

Calculate the standard deviation of the sample data shown to two decimal places X 5 8 11 9 4 19 7 5 7 29 9 29 6

Calculate the 5th percentile of the data shown X 1 6 14 8 19 4 20 2 21 4 23 1 23 2 23 3 27 7 28 7

Approximately 27 of American adults do not own a credit card A random sample of 500 adults is asked Do you own a credit card Describe the sampling distribution of p the sample proportion of adults who do not own a credit card b What is the probability that in a random sample of 500 adults more than 30 do not own a credit card c What is the probability that in a random sample of 500 adults between 25 and 35 do not own a credit card d Would it be unusual for a random sample of 500 adults to result in 120 or fewer who do not own a credit card Why

The lengths of adult males hands are normally distributed with mean 195 mm and standard deviation is 7 3 mm Suppose that 48 individuals are randomly chosen Round all answers to 4 where possible a What is the distribution of N 195 1 0536 OF OF b For the group of 48 find the probability that the average hand length is less than 194 c Find the third quartile for the average adult male hand length for this sample size 195 71 d For part b is the assumption that the distribution is normal necessary Yes No o

Q8 The chances are 3 out of 4 that the weather tomorrow will be like the weather today Today is Sunday and is a sunny day a What is the probability that it will be sunny all weak b What is the probability that it will be sunny until Wednesday and not sunny on Thursday Friday and Saturday ANSWER a 0 18 b 0 059

The average production cost for major movies is 58 million dollars and the standard deviation is 19 million dollars Assume the production cost distribution is normal Suppose that 8 randomly selected major movies are researched Answer the following questions Give your answers in millions of dollars not dollars Round all answers to 4 decimal places where possible a What is the distribution of X X NO 58 b What is the distribution of N 58 6 7175 O OB c For a single randomly selected movie find the probability that this movie s production cost is between 55 and 59 million dollars 19 0 OF d For the group of 8 movies find the probability that the average production cost is between 55 and 59 million dollars

A retirement confidence survey of 1000 workers and retirees in the united states 25 years of age and older conducted by Employee Benefit Research Institute in January 2014 found that 496 had less than 10 000 in savings a Obtain a point estimate for the population proportion of workers and retirees in the US 25 years of age and older who have less than 10 000 in savings b Verify that the requirements for constructing a confidence interval about p are satisfied C Construct a 95 confidence interval for the population proportion of workers and retirees in the US 25 years of age and older who have less than 10 000 in savings d Interpret the interval

6 x 1 2 x 5 A

6 2x 5 3x 10

3 5 x 8 7 23

5 4x 6 6x 20 A

3 x 1 11 2 x 13

10 3x 2 4x 2 2 6x 1 S

5x 7 x 1 9 A IT

Directions Solve graph and express the following inequalities in interval notation GRAPH INTERVAL NOTATION SOLVE 1 3x 12 6x 9

7 2 x 3 5x 9x 14

x 5x 6 12 A

11 The table below shows the results of a survey that asked 1051 adults from a certain country if they would support a change in their country s flag A person is selected at random Complete parts a through d Total D 492 559 1051 Males Females Total Support 163 245 408 Oppose 321 295 616 Unsure 8 19 27 a Find the probability that the person opposed the change or is female P opposed the change or is female Round to the nearest thousandth as needed b Find the probability that the person supports the change or is male P supports the change or is male Round to the nearest thousandth as needed c Find the probability that the person is not unsure or is female P is not unsure or is female Round to the nearest thousandth as needed d Are the events being male and support mutually exclusive Explain OA No because there are 163 males that support the change OB No because one can t be male and support the change at the same time OC Yes because one can t be male and support the change at the same time O D Yes because there are 163 males that support the change