Probability Questions and Answers

26 Factory A produces 4 6 10 bolts a year and Factory B produces 6 3 10 bolts a year a What is the total number of bolts produced by these two factories b How many more bolts did Factory B produce than Factory A Total number of bolts produced Difference in the number of bolts produced DRAG DROP THE ANSWER 21 107 1 09 10 1 7 10 2 1 108 17 10 6

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

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

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

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

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

6 x 1 2 x 5 A

5 4x 6 6x 20 A

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

10 The table below shows the number of male and female students enrolled in nursing at a university for a certain semester A student is selected at random Complete parts a D Nursing majors Non nursing majors 1019 96 600 1722 696 2741 Total Males 1115 Females 2322 Total 3437 a Find the probability that the student is male or a nursing major P being male or being nursing major Round to the nearest thousandth as needed b Find the probability that the student is female or not a nursing major P being female or not being a nursing major Round to the nearest thousandth as needed c Find the probability that the student is not female or a nursing major P not being female or being a nursing major Round to the nearest thousandth as needed d Are the events being male and being a nursing major mutually exclusive Explain OA No because there are 96 males majoring in nursing OB No because one can t be male and a nursing major at the same time OC Yes because there are 96 males majoring in nursing OD Yes because one can t be male and a nursing major at the same time

The amount of syrup that people put on their pancakes is normally distributed with mean 62 mL and standard deviation 11 mL Suppose that 40 randomly selected people are observed pouring syrup on their pancakes Round all answers to 4 decimal places where possible a What is the distribution of X X NO 61 5 b What is the distribution of N c If a single randomly selected individual is observed find the probability that this person consumes is between 64 2 mL and 65 9 mL d For the group of 40 pancake eaters find the probability that the average amount of syrup is between 64 2 mL and 65 9 mL e For part d is the assumption that the distribution is normal necessary Yes No

Question 4 of 14 4 A coin is tossed 1300 times and tails is observed in 702 of the tosses What is the empirical probability of heads Answer Previous Answer 46

stal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery Plasma volume is influenced by the overall health and physical activity of an dividual Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x 37 5 ml kg milliliters plasma per kilogram body weight Assume that a 7 80 ml kg for e distribution of blood plasma a Find a 99 confidence interval for the population mean blood plasma volume in male firefighters What is the margin of error Round your answers to two decimal places lower limit upper limit margin of error b What conditions are necessary for your calculations Select all that apply On is large the distribution of volumes is uniform o is known Oo is unknown the distribution of volumes is normal c Interpret your results in the context of this problem O The probability that this interval contains the true average blood plasma volume in male firefighters is 0 01 O We are 99 confident that the true average blood plasma volume in male firefighters falls within this interval We are 1 confident that the true average blood plasma volume in male firefighters falls within this interval The probability that this interval contains the true average blood plasma volume in male firefighters is 0 99 d Find the sample size necessary for a 99 confidence level with maximal margin of error E 2 70 for the mean plasma yolume in male firefighters

Bet of Filles per galloh MPG for 60 foreign cars is given in the following frequency table Find the mean median and mode for these data 20 21 MPG Frequency 5 2 19 2 OA The median is Find the mean Select the correct choice below and fill in any answer boxes in your choice Use a comma to separate answers as needed OB There is no median for these data 22 4 OA The mode s is are 23 6 OA The mean is approximately Type an integer or decimal rounded to the nearest tenth as needed Use a comma to separate answers as needed OB There is no mean for these data Find the median Select the correct choice below and fill in any answer boxes in your choice Find the mode Select the correct choice below and fill in any answer boxes in your choice Use a comma to separate answers as needed B There is no mode for these data 24 7 25 8 26 8 27 3 28 7 29 5 30 3

1 7 2n 1 3 9 9 m 12 1 2 1 3 1 1 20 5

EQUATIONS 5 m 1 2 9m 5 2 x 10 7

3 Determine whether the following statement is true or false If it is false explain why The probability that event A or event B will occur is P A or B P A P B P A or B Choose the correct answer below A True OB False the probability that A or B will occur is P A or B P A P B OC False the probability that A or B will occur is P A or B P A P B O D False the probability that A or B will occur is P A or B P A P B P A and B

First you ll have to calculate the SEM Use the values provided and the formula in the book lecture to calculate the SEM Put your value below Round your response out to two decimal places

A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 156 yellow peas a Construct a 95 confidence interval to estimate of the percentage of yellow peas b Based on the confidence interval do the results of the experiment appear to contradict the expectation that 25 of the offspring peas would be yellow a Construct a 95 confidence interval Express the percentages in decimal form 0 262 p 0 264 Round to three decimal places as needed b Based on the confidence interval do the results of the experiment appear to contradict the expectation that 25 of the offspring peas would be yellow No the confidence interval includes 0 25 so the true percentage could easily equal 25 OYes the confidence interval does not include 0 25 so the true percentage could not equal 25

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects After treatment with the drug 13 subjects had a mean wake time of 91 8 min and a standard deviation of 42 8 min Assume that the 13 sample values appear to be from a normally distributed population and construct a 90 confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments Does the result indicate whether the treatment is effective Find the confidence interval estimate www min o min Round to two decimal places as needed Does the result indicate whether the treatment is effective A Yes the confidence interval indicates that the treatment is not effective because the interval contains 0 minutes OB No the confidence interval does not indicate whether the treatment is effective OC Yes the confidence interval indicates that the treatment is not effective because the interval does not contain 91 8 minutes OD Yes the confidence interval indicates that the treatment is effective because the interval does not contain 0 minutes OE Yes the confidence interval indicates that the treatment is effective because the interval contains 0 minutes OF Yes the confidence interval indicates that the treatment is effective because the interval does not contain 91 8 minutes G Yes the confidence interval indicates that the treatment is not effective because the interval does not contain 0 minutes

Express the confidence interval 0 555 p 0 999 in the form pt E p E H

Describe what is misleading in the visual display of data below Marijuana Use Among College Students in the Last 30 Days Never Used 29 3 Not in Last 30 Days 10 Used 1 9 Days 5 5 Used 10 29 Days 3 5 Used All 30 Days 1 7 This question 1 point s possible Choose the correct answer below available until you s OA The title does not explain what is being displayed OB Colors on the chart are too light and distort the data OC The chart is too small O D The percentages do not add up to 100

A random sample of 20 adults in a particular country were asked to state what type of they use The results are in the table below None None None Condom Condom Condom Condom Condom Other None None Other None Condom Other None Pill Other Condom a Since data were collected for Select an answer variable s the correct graph to make is a Select an answer b Complete the frequency relative frequency table Birth Control Type None Pill None None Frequency Other c Which of the following is the correct bar chart for the given data Relative Frequency

The table below shows the gender distribution of students responding to the survey Use the table below to answer the following Over 3 0 2 0 3 0 Under 2 0 117 85 136 102 253 187 If one student is chosen at random what is Male Female Total The probability they are Female AND got Over a 3 0 use 4 decimals The probability they are Male OR got Under 2 0 use 4 decimals 38 36 74 Total 240 274 514

Rewrite this number in appropriate scientific notation 0 0000875 answer

Compute the exact values 3 3 5

Evaluate 24

Evaluate 6 32 8 3 2

Estimate the V139 Pick the closest estimate 011 0 11 5 011 2 012 O 11 8

Round 9 2506 to the nearest thousandth

Determine the required value of the missing probability to make the distribution a discrete probability distribution P 4 Type an integer or a decimal X 3 4 LO 5 6 P x 0 24 0 37 0 23

In the following probability distribution the random variable x represents the number of activities a parent of a K to 5th grade student is involved in Complete parts a through f below X P x 0 1 0 446 0 063 between 0 and 1 inclusive a Verify that this is a discrete probability distribution This is a discrete probability distribution because the sum of the probabilities is less than or equal to 1 2 3 t 0 276 0 137 greater than 0 and less than 1 4 0 078 and each probability is

3 Find the following percentiles for a chi square distribution with df a X 05 b X 01 C X 95 d X 025 e X 03 f v

55 57 596d 63 p 203 205 3 5 6 11cd 13d 1 A study was done on the relationship between high school grade point average GPA and scores on the SAT The following 8 scores were from a random sample of students taking the exam GPA SAT 3 2 725 3 8 752 3 9 745 3 3 680 b Interpret the residual that you calculated in part a B 3 6 700 The least squares regression line for predicting SAT from GPA was calculated to be y 154 158x a Calculate the residual for the student who had a GPA of 3 2 C P value 0 1974 2 8 562 2 Which residual plot below indicates that the linear model is appropriate Justify your answer A D friend 2 9 595 Dependent variable is Other R squared 87 3 s 3 853 with 11 2 9 degrees of freedom Variable Coefficient SE Coeff t ratio Intercept 306780 1 39 7 85 0 0001 2204 Marijuana 0 615003 0 0784 b Identify and interpret the coefficient of determination 3 5 730 3 The European School Study Project on Alcohol and Other Drugs published in 1995 investigated the use of marijuana and other drugs Data from 11 countries are summarized in the following scatterplot and regression analysis They show the association between the percentage of a country s ninth graders who report having smoked marijuana and who have used other drugs such as LSD amphetamines and cocaine c Identify and interpret the standard deviation of the residuals s a Write the equation of the least squares regression line

The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph More college graduates had starting salaries in the 61 000 65 000 range than in the 46 000 50 000 range Choose the correct answer below of Graduates Frequency 400 300 200 100 0 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars A True because the bar for 61 65 is taller than the bar for 46 50 B True because the sum of the heights of the first two bars in the graph is greater than the sum of the heigh of the last two bars C False because the bar for 61 65 is shorter than the bar for 46 50 O D False because the bar for 61 65 has the same height as the bar for 46 50

Determine whether the statement makes sense or does not make sense and explain your reasoning The graph shown below indicates that for the period from 2016 to 2019 the percentage of Americans whose educational attainment was high school graduate has rapidly increased of HS Graduates or More Educational Attainment in the United States 90 2 90 0 89 8 89 6 89 4 89 2 89 0 88 8 2015 2016 2017 2018 Year 2019 more Choose the correct answer below OA Yes the statement makes sense B No it does not make sense the time interval on the horizontal axis creates an overall impression of the percentage of Americans with a high school education or better increasing rapidly OC No it does not make sense the percentage of Americans with a high school education or better increased more rapidly during the period from 2015 2016 D No it does not make sense the scale on the vertical axis is stretched to create an overall impression of the percentage of Americans with a high school education or better increasing rapidly

A food safety guideline is that the mercury in fish should be below 1 part per million ppm Listed below are the amounts of mercury ppm found in tuna sushi sampled at different stores in a major city Construct a 98 confidence interval estimate of the mean amount of mercury in the population Does it appear that there is too much mercury in tuna sushi 0 52 0 73 0 10 0 95 1 29 0 58 0 93 What is the confidence interval estimate of the population mean 0 277 ppm 1 180 ppm Round to three decimal places as needed Does it appear that there is too much mercury in tuna sushi OA Yes because it is possible that the mean is not greater than 1 ppm Also at least one of the sample values exceeds 1 ppm so at least some of the fish have too much mercury OB No because it is not possible that the mean is greater than 1 ppm Also at least one of the sample values is less than 1 ppm so at least some of the fish are safe OC No because it is possible that the mean is not greater than 1 ppm Also at least one of the sample values is less than 1 ppm so at least some of the fish are safe OD Yes because it is possible that the mean is greater than 1 ppm Also at least one of the sample values exceeds 1 ppm so at least some of the fish have too much mercury

An IQ test is designed so that the mean is 100 and the standard deviation i 14 for the population of normal adults Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99 confidence that the sample mean is within 3 IQ points of the true mean Assume that o 14 and determine the required sample size using technology Then determine if this is a reasonable sample size for a real world calculation The required sample size is 145 Round up to the nearest integer Would it be reasonable to sample this number of students O No This number of IQ test scores is a fairly large number Yes This number of IQ test scores is a fairly large number No This number of IQ test scores is a fairly small number OYes This number of IQ test scores is a fairly small number

4 List the domain and the range of the graph of each function a 4 2 c 4 4 y 2 0 4 3 1 O 2 y N 4 X 4 b X 2 4 2 0 2 4 y 2 4 X

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects Before treatment 17 subjects had a mean wake time of 102 0 min After treatment the 17 subjects had a mean wake time of 95 3 min and a standard deviation of 21 8 min Assume that the 17 sample values appear to be from a normally distributed population and construct a 95 confidence interval estimate of the mean wake time for a population with drug treatments What does the result suggest about the mean wake time of 102 0 min before the treatment Does the drug appear to be effective Construct the 95 confidence interval estimate of the mean wake time for a population with the treatment min min Round to one decimal place as needed