Probability Questions and Answers

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 Using the binomial distribution the probability is 0 2225 Round to four decimal places as needed b What is the probability that among 16 randomly observed individuals fewer than 5 do not cover their mouth when sneezing Using the binomial distribution the probability is 0 5685 Round to four decimal places as needed c Would you be surprised if after observing 16 individuals fewer than half covered their mouth when sneezing Why Yes it would be surprising because using the binomial distribution the probability is which is less than 0 05

To produce x units of a religious medal costs C x 13x 60 The revenue is R x 33x Both cost and revenue are in dollars a Find the break even quantity b Find the profit from 440 units c Find the number of units that must be produced for a profit of 200 FO units is the break even quantity Type an integer

In a survey of 2341 adults 732 say they believe in UFOs Construct a 99 confidence interval for the population proportion of adults who believe in UFOs A 99 confidence interval for the population proportion is Round to three decimal places as needed Interpret your results Choose the correct answer below Route OA With 99 confidence it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interva B With 99 confidence it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval C With 99 probability the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval OR The endpoints of the giver confidence interval shows that 99 of adults believe in UFOS

Select all of the following indicators Answer

A quiz consists of 50 multiple choice questions each with five possible answers only one of which is correct If a student guesses on each question what is the mean and standard deviation of the number of correct answers Round to three decimal places O A mean 10 standard deviation 2 828 B mean 2 5 standard deviation 2 828 C mean 2 5 standard deviation 1 581 OD mean 10 standard deviation 1

Sixty five percent of men consider themselves knowledgeable soccer fans If 11 men are randomly selected find the probability that exactly three of them will consider themselves knowledgeable fans Round to three decimal places OA 0 010 OB 0 273 OC 0 650 OP 0225

The probability that a football game will go into overtime is 12 What is the probability that two of three football games will go to into overtime Round to three decimal places A 0 038 OB 0 120 OC 0 014 OD 0 279

Select all of the following indicators

Consider the discrete probability distribution given when answering the following question Find the probability that equals 4 X P x 3 0 02 A 0 66 O B 2 64 C 2 32 D 9 28 4 7 9 0 29 0 03

The graph of the discrete probability to the right represents the number of live births by a mother 49 to 54 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 0 239 0263 0 171 0 109 0 101 0 022 0 038 3 5 Number of Live Births 0 057 6 7 8 Q c What is the probability that a randomly selected 49 to 54 year old mother who had a live birth in 2015 has had her sixth or more live birth in that year 0 117 Type an integer or a decimal d If a 49 to 54 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 h

Use n 6 and p 0 6 to complete parts a through d below 5 0 1866 6 0 0467 Round to four decimal places as needed b Compute the mean and standard deviation of the random variable using x x P x ox X P x H Hx 3 6 Round to two decimal places as needed ox 1 2 Round to two decimal places as needed c Compute the mean and standard deviation using x np and ox np 1 P Round to two decimal places as needed Hx

Use n 6 and p 0 6 to complete parts a through d below a Construct a binomial probability distribution with the given parameters X P x 0 0 0041 0 0369 0 1382 3 0 2765 4 0 311 5 0 1866 6 0 0467 Round to four decimal places as needed b Compute the mean and standard deviation of the random variable using Hx x P x and Gx x P x H Hy Bound to two decimal places as needed 1 2

Fourteen jurors are randomly selected from a population of 4 million residents Of these 4 million residents it is known that 39 are of a minority race Of the 14 jurors selected 2 are minorities a What proportion of the jury described is from a minority race b If 14 jurors are randomly selected from a population where 39 are minorities what is the probability that 2 or fewer jurors will be minorities c What might the lawyer of a defendant from this minority race argue a The proportion of the jury described that is from a minority race is 0 14 Round to two decimal places as needed b The probability that 2 or fewer out of 14 jurors are minorities assuming that the proportion of the population that are minorities is 39 is Round to four decimal places as needed

polynomial function is given R x x 4x 4x a Describe the end behavior of the polynomial function End behavior y 3 b Match the polynomial function with one of the following graphs y 2 1 10 5 10 as x 00 10 as x 3 X 3 2 10 10 y 10 X

An ord spots Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together This sum is recorded as the outcome of a single trial of a random experiment Compute the probability of each of the following events 123456 Event A The sum is greater than 9 Event B The sum is divisible by 5 or 6 or both Round your answers to two decimal places P A P B Question 9 of 15 Fran the Fearless has a well known act at a local zoo As part of the act Fran handles a scary animal that she picks at random out of the Box of Terror The following animals are in the box 11 poisonous snakes 8 nonpoisonous snakes 12 poisonous spiders and 10 nonpoisonous spiders What is the probability that the animal Fran picks is nonpoisonous or is a snake Do not round intermediate computations and round your answer to the nearest hundredth Question 10 of 15 Let A and B be two events such that P A 0 28 and P B 0 24 Do not round your responses a Determine P A U B given that A and B are mutually exclusive b Determine P AUB given that A and B are independent 0 28 0 24 0 52 0 52

exclusive Suppose event A occurs with probability occurs with probability 0 06 1t mobnst te bozeldza Compute the following fed a Compute the probability that B occurs but A does not occur b Compute the probability that either A occurs without B occurring or B occurs without A occurring Question 12 of 15 of the people who fished at Clearwater Park today 42 had a fishing license and 28 did not Of the people who fished at Mountain View Park today 42 had a license and 18 did not No one fished at both parks Suppose that one fisher from each park is chosen at random What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license Do not round your answer Mis Question 13 of 15 A university class has 23 students 9 are art majors 6 are nursing majors and 8 are psychology majors The professor is planning to select two of the students for a demonstration The first student w be selected at random and then the second student will be selected at random from the remaining students What is the probability that two art majors will be selected Do not round your intermediate computations Round your final answer to three decimal places Question 14 of 15 At a certain college 49 of the students are female and 19 of the students major in civil engineering Furthermore 10 of the students both are female and major in civil engineering Answer the questions below a What is the probability that a randomly selected female student majors in civil engineering Round your answer to 2 decimal places b What is the probability that a randomly selected civil engineering major is female Round your answer to 2 decimal places

8 According to the manufacturer the normal output voltage for a particular device is 120 volts 1 point From a sample of 40 devices the mean was found to be 123 59 volts and the standard deviation was 0 31 Jolt The test statistic was then found to be 73 242 Use the test statistic and a 0 05 significance level to test the claim that the Sample is from a population with a mean equal to 120 volts State the initial and final conclusion Reject the null hypothesis there is not sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts Reject the null hypothesis there is sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts Fail to reject the null hypothesis there is sufficient evidence to warrant a rejection of the claim that the mean voltage is greater than 120 volts Fail to reject the null hypothesis there is not sufficient evidence to warrant a rejection of the claim that the mean voltage is greater than 120 volts 9 A simple random sample of 10 pages from a dictionary is obtained and the number of defined words on each page is recorded The sample mean is found to be 53 5 definitions per page and put voltage is 120 volts Data Set to have Han 1 point

29 O 40 33 The first quartile Q1 value from the above box plot is O 29 33 O 52 40 52 70

The mean of any standard normal distribution is O 1 O 0 5 O 0 5 O 0

Consider the histogram showing the weights of babies born in a hospital over a month Weight of Babies Number of Babies 4 2 1 04 4 O 12 5 How many babies are less than 6 pounds 6 7 Weight in pounds 8 9 10

The dot plot below shows the number of songs Carly downloaded over 15 successive weekends 08 4 O 5 5 6 What is the greatest number of songs downloaded 8 7 Number of Songs 9 10 11

This scatterplot shows the number of hours a student slept every night and his or her grade point average Grade Point Average 4 0 3 5 3 0 2 5 2 0 1 5 1 0 0 5 0 02 08 O 1 GPA vs Hours of Sleep 2 3 4 5 6 Hours of Sleep 7 The equation for the least squares regression line to this data is 0 375x 1 33 What is the predicted GPA for a student who sleeps 2 5 hours per day Answer choices are rounded to the hundredths place 8 9

A credit card company surveys 125 of its customers to ask about satisfaction with customer service The results of the survey divided by gender are shown below O 0 81 O 0 19 O 0 5 O 0 13 Extremely Satisfied 0 29 Satisfied Neutral Dissatisfied Extremely Dissatisfied Males 25 21 13 9 2 Females 7 If a survey is selected at random what is the probability that the person is a female with neutral feelings about customer service Answer choices are rounded to the hundredths place 13 16 14 5

O What is the theoretical probability of drawing a king from a well shuffled deck of 52 cards 1 26 4 13 03 122 O 52 D

Peter analyzed a set of data with explanatory and response variables x and y He concluded the mean and standard deviation for x as 7 8 and 3 70 respectively He also concluded the mean and standard deviation for y as 12 2 and 4 15 respectively The correlation was found to be 0 964 Select the correct slope and y intercept for the least squares line Answer choices are rounded to the hundredths place O O O O Slope 1 08 y intercept 3 78 Slope 1 08 y intercept 3 78 Slope 1 08 y intercept 3 78 Slope 1 08 y intercept 3 78

Use the data in the Stem L STEM LEAF 015 113 256 3302 4974

Which of the following is not a characteristic of t distribution O Depends on degrees of freedom O It tends to be flatter and have heavier tail than normal distribution Mean of 1 O For large samples the t and z distributions are nearly equivalent O Symmetric distribution

A correlation coefficient between average temperature and ice cream sales is most likely to be O between 1 and 2 O between 1 and 2 O between 0 and 1 O between 0 and 1

Which of the following is NOT a guideline for establishing causality O Look for cases where correlation exists between the variables of a scatterplot O Perform a randomized controlled experiment O Take into consideration all the other possible causes O Keep all variables the same to get duplicate results

Fred Anderson an artist has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day He has made a scatter plot to depict the relationship between the number of hours and the number of visitors Number of Visitors at Exhibit Number of Visitors O21 18 O 1 16 14 12 10 00 6 4 2 0 0 1 2 How many visitors were there during the fourth hour 3 4 5 Number of Hours 6 7 8 9

Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of 0 4 0 2x What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable O The price of the soap decreases by 0 40 on average when the thickness increases by 1 cm The price of the soap decreases by 0 20 on average when the thickness increases by 1 cm O The price of the soap increases by 0 40 on average when the thickness increases by 1 O cm The price of the soap increases by 0 20 on average when the thickness increases by 1 O cm

1 20 30 QUESTION 14 and 70 Given X 100 98 81 78 78 94 82 96 96 77 78

Determine whether or not the given procedure Spinning Answer

Question 12 What is the difference between disposable and discretionary income Points 1 Disposable income is primarily used to satisfy needs while discretionary income is used to supply wants Discretionary income is primarily used to satisfy needs while disposable income is used to supply wants Disposable income is primarily used to pay taxes while discretionary income is used to supply wants and needs Discretionary income is primarily used to pay taxes while disposable income is used to supply wants and needs Complete

Question 9 Points 2 How would you categorize direct foreign investment in the United States As the amount of foreign purchases of U S real estate and businesses foreign investment is part of the world economy As the amount of foreign purchases of U S real estate foreign investment is part of the world economy Direct foreign investment in the U S is dependent on the political good will of foreign countries and trade agreements Direct foreign investment in the U S is dependent on the weakness of the U S dollar and the tax status of foreign workers living in the U S

Study the following list CITGO Ben Jerry s Ice Cream Trader Joe s A P Supermarkets Which of the following choices are the companies in the list an example of O Domestic investments O Direct foreign investment O American owned businesses which receive foreign investment Publicly owned companies

Given the following discrete uniform probability distribution find t decimal places if necessary Answer

square root of the proportion of the total varia a and c QUESTION 4 correlation of r 0 60 exists between a set of stributions the value of r will D remain the same Dwill increase O decrease be less meaningful

STION 6 ation implies causation e Ise JESTION 7 positive relationship b is negative b is positive a must be positive a must be negative

Determine whether or not the following distribution is a pro satisfied by the distribution Answer

If n 140 and p p hat 0 4 construct a 95 confidence interval Give your answers to three decimals Question Help

A psychologist is interested in constructing a 99 confidence interval for the proportion of people who accept the theory that a person s spirit is no more than the complicated network of neurons in the brain Of those randomly selected 58 of the 713 people agreed with this theory a With 99 confidence the proportion of all people who accept the theory that a person s spirit is no more than the complicated network of neurons in the brain is between and Round to 3 decimal places b If many groups of 713 randomly selected people are surveyed then a different confidence interval would be produced from each group About percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person s spirit is no more than the complicated network of neurons in the brain and about percent will not contain the true population proportion

Random Phenome Step 3 of 3 What is Answer

Random Phenomenon Observe the r Step 1 of 3 Identify the random varia Answer

One condition for performing a hypothesis test is that the observations are independent Mary is going to take a sample from a population of 500 students How many students will Mary have to sample without replacement to treat the observations as independent O 300 O100 O 50 O 490

Which of the following is a guideline for establishing causality O Check if the effect is present when the response variable is absent Look for cases where correlation exists between the variables of a scatterplot O Keep all variables the same to get duplicate results Do not consider other possible causes

3 4 points Students take lecture quizzes in EAS 305 classes Meanwhile some students that use mobile devices have been having issues submitting their answers The instructor suspects that the issue may be related to the operating system OS on the devices Out of the 39 students that use mobile devices to take their quizzes 18 use Mac OS 13 use Android OS and the rest use Windows OS The instructor randomly selected 3 students from the 45 students as a sample for analysis a 1 5 points Find the probability that all 3 students use the same OS b 1 point Determine the probability all OS are contained in the sample 1 5 points Determine the probability that at least one of the students in the sample use Os or Windows OS

Two sets A and B are shown in the Venn diagram below 8 Which statement is TRUE O Set A has 8 elements A O Set B has 7 elements 3 O There are a total of 2 elements shown in the Venn diagram 2 B 7

Which of the following is an example of a false positive O Test results indicate that a patient does not have cancer when in fact he does O Test results indicate that a patient has cancer when in fact he does not O Test results confirm that a patient does not have cancer Test results confirm that a patient has cancer

Three hundred students in a school were asked to select their favorite fruit from a choice of apples oranges and mangoes This table lists the results O 0 39 O 0 13 O 0 25 Apple Orange 0 75 Mango Boys 66 52 40 Girls If you were to choose a boy from the group what is the probability that mangoes are his favorite fruit Answer choices are rounded to the hundredths place 46 41 55