Probability Questions and Answers

For a standard normal distribution find P Z c 0 5761 Find c rounded to two decimal places

Many high schools now have drug testing programs for athletes The main goal of these programs is to reduce the use of banned substances by students who play sports It is not practical to test every athlete for drug use regularly Instead school administrators give drug tests to randomly selected student athletes at unannounced times during the school year Students who test positive face serious consequences including letters to their parents required counseling and suspension from athletic participation Drug tests aren t perfect Sometimes the tests say that athletes took a banned substance when they did not This is known as a false positive Other times drug tests say that athletes are clean when they did take a banned substance This is called a false negative Suppose that 16 of the high school athletes in a large high school have taken a banned substance The drug test used by this high school has a false positive rate of 5 and a false negative rate of 10 The student Mr Brenes was randomly selected and tested positive It your job to defend him at a school board hearing You should do the following 1 Create a sample space for this scenario 2 Calculate appropriate probabilities as well as conditional probabilities Think about what data you would could use to their innocence

40 A 70 80 50 60 Which statement must be true 90 100 Each distribution has a different mean and the same standard deviatio Each distribution has a different mean and a different standard deviatic Each distribution has the same mean and the same standard deviation Each distribution has the same mean and a different standard deviation

For a standard normal distribution find the approximate value of P 0 78 z 1 16 Use the portion of the standa normal table below to help answer the question 22 66 78 Z 0 00 0 16 0 22 0 78 1 00 1 16 1 78 2 00 Probability 0 5000 0 5636 0 5871 0 7823 0 8413 0 8770 0 9625 0 9772

QUESTIVIT Suppose a car salesman records the number of cars he sold for 15 weeks The following frequency table summarizes the results What is the five number summary Number of Cars Sold 3 5 6 78 10 11 12 Frequency 1 221 3 3 1 2 Il

1 of women of age 40 who participate in routine screenings have breast cancer 80 of women with breast cancer will get positive mammogra phies 10 of women without breast cancer will also get positive mam mographies A woman in this age group had a positive mammography in a routine screening Is it likely that she actually has breast cancer

A probability experiment consists of rolling a fair 16 sided die Find the probability of the event below rolling a 10 The probability is Tyne an integer or decimal rounded to three decimal places as needed

The probability that an event will happen is P E 0 38 Find the probability that the event will not happen The probability that the event will not happen is Simplify your answer

A probability experiment consists of rolling a fair 8 sided die Find the probability of the event below rolling a number greater than 3 The probability is Type an integer or decimal rounded to three decimal places as needed

The probability that an event will not happen is P E 0 81 Find the probability that the event will happen The probability that the event will happen is Simplify your answer

1 The probability that an event will not happen is P E Find the probability that the event will happen 14 The probability that the event will happen is Type an integer or a simplified fraction

Federal Income Taxes and Piecewise Functions LC The graph of a piecewise function is shown 7 6 5 4 3 4 O 2 u 1 0 2 0 1 0 01 00 00 0 00 00 2 1 6 5 4 3 2 1 0 2 3 4 Ty 5 6 What is the domain of the function 3 4 5 6

It is believed that standardized test scores such as SAT is a good predictor of first year college students GPA X y 1200 1120 1000 1420 3 2 2 5 2 7 3 5 2 9 1280 750 1100 2 2 2 3 1 Find the the correlation coefficient Round your final answer to four decimal places T 2 Write the regression equation below Round all numbers to four decimal places 3 Using the data shown above predict a student s first year GPA when the student scores a 1275 on the SAT Round your final answer to two decimal places 4 What percentage of variation in GPAS can be explained by students SAT scores Round your final answer to two decimal places

The state of CT claims that the average time on death row is 15 years A random survey of 75 death row inmates revealed that the average length of time on death row is 16 9 years with a standard deviation of 6 years Conduct a hypothesis to test the state of CT s claim What type of test should be run O t test of a mean Oz test of a proportion The alternative hypothesis indicates a Oright tailed test O two tailed test O left tailed test Calculate the p value What is the decision Owe fail to reject the claim that the average time on death row is 15 years We reject the claim that the average time on death row is 15 years

Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA X y 10 3 0 1 5 2 4 3 2 2 3 5 5 4 7 2 7 3 2 1 1 Find the the correlation coefficient Round your final answer to four decimal places T 2 Write the regression equation below Round all numbers to four decimal places 3 Using the data shown above predict a student s GPA when the student plays video games for 15 hours each week Round your final answer to two decimal places 4 What percentage of variation in GPAS can be explained by the number of hours students play video games each week Round your final answer to two decimal places

You run a regression analysis on data with two variables and you obtain the regression equation y 3 225x 27 777 with a correlation coefficient of r 0 625 You want to predict the value for the response variable for a value of 130 as the explanatory variable What is the predicted response value y Report answer accurate to one decimal place Question Help Bort t

3 12 Simplifying Trigonometric Expressions Write the trigono metric expression in terms of sine and cosine and then simplify 3 cos t tan t 4 cos t csc t 5 sin 0 sec 0 6 tan 0 csc 0 7 tan x sec x 8 sec x CSC X

The population of a pigeons in a city is 210 and is growing exponentially at 17 per year Write a function to represent the population of pigeons after t years where the monthly rate of change can be found from a constant in the function Round all coefficients in the function to four decimal places Also determine the percentage rate of change per month to the nearest hundredth of a percent Function f t

Match the experimental probabilities with the methods by which they could have been obtained Hint think about the theoretical probabilities of each Getting heads when flipping a coin Randomly choosing an ace from a standard deck of 52 cards Rolling a number greater than 1 on a six sided number cube Choose Choose Choose Choose

Two bus companies run services between Los Angeles and San Francisco The mean journey times and standard deviations in those times are given below If Samantha needs to travel between the cities which company should she choose if Mean Time hours Standard Deviation hours Inter Cal Express 9 5 0 25 She needs to catch a plane in San Francisco hint consistency is important She travels weekly to visit friends who live in San Francisco and wishes to minimize the time she spends on a bus over the entire year Choose Choose Choose Inter Cal Fast Dog Fast dog Travel 8 75 2 5

17650 31150 26550 35350 23600 8050 24100 10150 11350 11950 Question 12 Find the sample standard deviation of the data Round two decimal places 1 pts

places 64 6 28 36 4 8 8 15 49 2 63 6 57 4 20 2 Question 10 Find the sample standard deviation of the data Round two decimal places 20 4 33 1 pt

Use this data to complete the following question The Pacific Ocean group had weights of 126 kg 130 kg 135 kg 136 kg 137 kg 140 kg 148 kg 150 kg What is the midrange O 16 O 150 O 138 O 24

King queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards were well shuffled A single card is selected randomly from the remaining deck The probability of getting a club is O 10 49 4 13 49 O 5 26

A coin is tossed 3050 times and tails occur 1025 times Find the experimental probability of getting tails O 0 789 O 0 336 O 0 543 O 0 102

The letters that form the word MISSISSIPPI are placed in a bowl What is the probability of choosing a P Enter your answer in reduced fraction form Example 1 2

A coin is tossed 20 times In 12 of the flips heads appeared Find the experimental probability of getting heads O 5 12 11 2

A single card is randomly drawn from a deck of 52 cards Match each of the given cards with the probability that it is drawn The King of Diamonds A King A spade Choose Choose 4 52 1 4 1 52 Choose

In a deck of 52 playing cards what is the probability of drawing a spade Enter your answer in reduced fraction form Example 1 2

9 pts There were 2430 Major League Baseball games played in 2009 and the home team won the game in 53 of the games If we consider the game played in 2009 as a sample of all MLB games test to see if there is evidence at the 5 level that the home team wins more than half the games Show all steps of the hypothesis test to receive points

ents A and B are mutually exclus mpute the following necessary consult a list of form a Compute the probability tha

2 3 4 is tossed three times An outcome is repres in the table below Note that each outcome ch of the three events in the table check th

An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time Suppose the mean time between occurrences of loads is 0 4 year a How many loads can be expected to occur during a 4 year period loads b What is the probability that more than eleven loads occur during a 4 year period Round your answer to three decimal places c How long must a time period be so that the probability of no loads occurring during that period is at most 0 2 Round your answer to four decimal places yr You may need to use the appropriate table in the Appendix of Tables to answer this question

An instructor who taught two sections of engineering statistics last term the first with 25 students and the second with 35 decided to assign a term project After all projects had been turned in the instructor randomly ordered them before grading Consider the first 15 graded projects a What is the probability that exactly 10 of these are from the second section Round your answer to four decimal places b What is the probability that at least 10 of these are from the second section Round your answer to four decimal places c What is the probability that at least 10 of these are from the same section Round your answer to four decimal places d What are the mean value and standard deviation of the number among these 15 that are from the second section Round your mean to the nearest whole number and your standard deviation to three decimal places mean standard deviation projects projects e What are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section Round your mean to the nearest whole number and your standard deviation to three decimal places mean standard deviation projects projects

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a 8 per hour so that the number of arrivals during a time period of t hours is a Poisson rv with parameter 8t Round your answers to three decimal places a What is the probability that exactly 6 small aircraft arrive during a 1 hour period What is the probability that at least 6 small aircraft arrive during a 1 hour period What is the probability that at least 11 small aircraft arrive during a 1 hour period b What is the expected value and standard deviation of the number of small aircraft that arrive during expected value standard deviation c What is the probability that at least 27 small aircraft arrive during a 2 5 hour period What is the probability that at most 17 small aircraft arrive during a 2 5 hour period You may need to use the appropriate table in the Appendix of Tables to answer this question 90 min period

A certain type of flashlight requires two type D batteries and the flashlight will work only if both its batteries have acceptable voltages Suppose that 90 of all batteries from a certain supplier have acceptable voltages Among ten randomly selected flashlights what is the probability that at least nine will work Round your answer to three decimal places USE SALT What assumptions did you make in the course of answering the question posed We have assumed here that the batteries voltage levels are independent We have assumed here that the batteries voltage levels are dependent

weights the pumpk while they are gro growing giant pur lifficult to weigh a large pumpkin before it is harvested so a method has been developed for estimating the weight The grower measures around the pumpkin oth horizontally and vertically then adds the results This is called the OTT over the top measurement and is used to predict the weight of the pumpkin ollowing are the OTT measurements and actual weights of the 10 largest pumpkins entered into official competitions in a recent year OTT inches Weight pounds 469 0 480 0 Part 1 of 4 452 0 465 0 490 0 451 0 454 0 477 0 462 0 490 0 Send data to Excel Part 0 4 2469 0 2416 5 2136 0 2152 0 2528 0 2114 0 2138 9 2157 5 2070 2433 9

Question 5 X P X a Find the mean of this probability distribution Roun 0 0 15 1 0 25 b Which is the correct interpretation of this mean val A O The predicted value of the next outcome with t O The average value of many outcomes with these c Find the variance of this probability distribution Ro

P Question 19 A survey reports that the probability a person has blue eye selected at Miramar College and asked if they have blue ey a Find the probability that exactly 3 of them have blue ey b Find the probability that exactly 2 of them have blue ey c Find the probability that at least 1 of them has blue eye d Find the probability that more than 2 have blue eyes Ro

In 1993 there were approximately 10 000 fast food outlets in the US that specialized in Mexican food Of these the largest were Taco Bell with 4812 outlets Taco John s with 440 outlets and Del Taco with 267 outlets Q The relative frequency that a fast food outlet that specializes in Mexican food is either Taco Bell or Taco John s is P E Check P E Hint Answer should be accurate to 4 decimal places QThe relative frequency that a fast food outlet that specializes in Mexican food is none of the three named outlets is Check Hint Answer should be accurate to 4 decimal places

You are playing cards and are dealt a hand of six cards from a standard deck of 52 QWhich two of the following are possible sample spaces You must click on the two correct answers consecutively otherwise you will lose points and health A P 52 6 B C 52 6 C The set of permutations of 6 cards chosen from 52 D P 6 52 E The set of combinations of 6 cards chosen from 52 F The number of combinations of 6 cards chosen from 52 G C 6 52

oot temperatures Foot ulcers are a common problem for people with diabetes Higher skin temperatures on the foot indicate an increased risk of ulcers In tudy performed at the Colorado School of Mines skin temperatures on both feet were measured in degrees Fahrenheit for 8 diabetic patients The results an resented in the following table Use a TI 84 Plus calculator to answer the following Left Foot Right Foot 88 89 89 90 89 86 87 82 78 78 89 87 80 80 85 85

Use the given confidence int 0 610 0 640 E Type an integer or a

The business college computing center wants to determine the proportion of business students who have laptop computers If the proportion differs from 30 then the lab will modify a proposed enlargement of its facilities Suppose a hypothesis test is conducted and the test statistic is 2 5 Find the p value for a two tailed test of the hypothesis O 0 0124 O 0 4876 O 0 0031 O 0 0062

A large university is interested in learning about the average time it takes students to drive to campus The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus This variable travel time was then used to conduct a test of the hypothesis The goal was to determine if the average travel time of all the university s students differed from 20 minutes Suppose the sample mean and sample standard deviation were calculated to be 23 2 and 20 26 minutes respectively Calculate the value of the test statistic to be used in the test 2 437 O 2 551 O 1 893

Express the following probability as a simplified fraction and as a decimal If one person is selected from the population described in the table find the probability that the person is not married Marital Status of a Certain Population Ages 18 or Older in Millions Male Female Total Married 69 70 139 Never Married 35 29 64 Divorced Widowed Total 11 2 117 16 8 123 27 10 240

Experim 3 Suppose 75 tagged rainbow trout were released into the Lower Saluda River below the Lake Murray Dam Fishermen reported catching 10 30 and 80 rainbow trout Based on the number of tagged fish caught find the estimated population and enter the results below Then find the percent error Number of fish caught 10 30 80 Number of Estimated tagged Population fish in Rounded catch 3 6 13 250 375 461 Actual Population 395 395 395 Percent Error Round to the nearest percent 36 x 5 18 65

We can assume that there are 430 blue id 6788437 marbles 370 purple marbles 600 red marbles 960 white marbles and 640 yellow marbles If we add the results how many marbles do we have We have marbles What law states that if our sample size is large enough our results should be close to the theoretical probability The Law of Large If we took another sample conducted another experiment do you think we would get the exact same results Click to view answer What is the only way to know exactly how many of each color are in the bag We need to conduct a n

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product The selling price for the product will be 45 per unit Probability distributions for the purchase cost the labor cost and the transportation cost are estimated as follows Procurement Cost 10 11 12 Probability Labor Cost Probability Cost 0 25 0 45 0 3 20 22 24 25 Profit per unit for best case 0 1 0 25 Mean profit per unit 0 35 Transportation 0 3 3 a Compute profit per unit for base case worst case and best case Profit per unit for base case Profit per unit for worst case 5 b Construct a simulation model to estimate the mean profit per unit If required round your answer to the nearest cent Probability 0 75 0 25 c Why is the simulation approach to risk analysis preferable to generating a variety of what if scenarios d Management believes that the project may not be sustainable if the profit per unit is less than 5 Use

According to the New York State Board of Law Examiners approximately 68 of people taking the New York Bar Exam passed the exam Use this information to find the following probabilities Round solutions to four decimal places if necessary 1 If 10 people who have taken the New York Bar Exam are randomly selected what is the probability that at least 75 have passed Round your answer to 4 decimal places P p 0 75 2 If 48 people who have taken the New York Bar Exam are randomly selected what is the probability that at least 75 have passed Round your answer to 4 decimal places P 0 75 3 Why did the probability decrease The probability decreased since the sample size decreased resulting in a wider distribution which increased the area of the right tail The probability decreased since the sample size increased resulting in a narrower distribution which reduced the area of the right tail