Probability Questions and Answers

On a particular day a restaurant that is open for lunch and dinner had 187 customers Each customer came in for one meal An employee recorded at which meal each customer came in and whether the customer ordered dessert The data are summarized in the table below Dessert No dessert Lunch 36 Dinner 34 28 89 Suppose a customer from that day is chosen at random Answer each part Do not round intermediate computations and round your answers to the nearest hundredth 0 If necessary consult a list of formulas a What is the probability that the customer came for dinner and did not order dessert b What is the probability that the customer came for dinner or did not order dessert X

An urn contains 5 black and 8 white balls Four balls are randomly drawn from the urn in succession with replacement That is after each draw the selected ball is returned to the urn What is the probability that all 4 balls drawn from the urn are black Round your answer to three decimal places If necessary consult a list of formulas

A spinner has 10 equally sized slices numbered from 1 to 10 Some are grey and some are white as shown below 9 8 7 10 1 65 0 2 3 4 Answer the following questions Write each answer as a fraction The wheel will be spun and will stop on a slice at random a What is the probability that the wheel stops on a white slice b What is the probability that the wheel stops on a white slice given that the wheel stops on a number less than 9 00 X

At a certain pizza parlor 36 of the customers order a pizza containing onions 32 of the customers order a pizza containing sausage and 17 order a pizza containing both onions and sausage Find the probability that a customer chosen at random will order a pizza containing onions or sausage or both Write your answer as a decimal not as a percentage If necessary consult a list of formulas

Suppose that 55 of the people who inquire about investments at a certain brokerage firm end up investing in stocks 45 end up investing in bonds and 68 end up investing in stocks or bonds or both What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds Write your answer as a decimal not as a percentage If necessary consult a list of formulas

A city planner surveyed 155 residents For each the planner recorded whether the resident owns a car and whether the resident lives alone The results are summarized in the table below Car Alone Not alone 31 No car 33 21 70 Suppose a resident from the survey is chosen at random Answer each part Do not round intermediate computations and round your answers to the nearest hundredth If necessary consult a list of formulas n a What is the probability that the resident does not own a car 0 b What is the probability that the resident does not own a car or lives alone X

We have a deck of 6 cards numbered from 1 to 6 Some are white and some are grey as shown below 123 4 5 6 Answer the following questions Write each answer as a fraction A card will be drawn at random a What is the probability that the number 5 card is drawn 0 b What is the probability that the number 5 card is drawn given that the Icard drawn is grey 0 00 X

Eight all 1 to 8 are placed in a bag Some are white and some are grey as shown below 1234 5678 Answer the following questions Write each answer as a fraction A ball will be randomly selected a What is the probability that the selected ball is grey 0 b What is the probability that the selected ball is grey given that an even numbered ball is selected X

Suppose a recent national survey reports that the mean height of adult males is 69 6 in with a standard deviation of 3 2 in im thinks that the mean height of adult males is shorter than reported He randomly collects the heights of 40 adult males and finds the mean height to be 68 8 in Select the correct null hypothesis Ho and the correct alternative hypothesis H Ho H

Suppose a recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10 9 ft A biologist observing a huge field of mature plants of this particular species of sunflower thinks that the mean height is shorter than reported He measures the heights of 55 randomly selected sunflowers and finds the mean height to be 10 6 ft Select the correct null Ho and alternative H hypotheses Ho H

Suppose that pregnancies for all women are known to have a mean duration of 282 days and a standard deviation of 9 3 days doctor wants to compare the duration of pregnancy for women who exercise to the duration of pregnancy for all women To this she selects a random sample of 82 pregnant women who exercise and finds that the mean duration of pregnancy for thes women is 283 days The doctor plans to use a one sample z test to determine whether or not the mean duration of pregnancy for women who exercise differs from the mean duration of pregnancy for all women Choose the appropriate null and alternative hypotheses for such a test O Ho 282 days and H 282 days Ho 282 days and H 282 days 283 days and H 283 days O Ho O Ho 282 days and H 282 days O Hox 282 days and H 282 days

Imagine that a tomato farmer wants to know how many tomatoes she should save this year to have enough seeds for next year s crop Historically she has obtained an average of 17 viable seeds per tomato She wants to check if the number of viable seeds for this year s crop is any different from the average Because she does not have any preconceived notions of why this year s crop would be more or less viable than her past crops she decides to answer her question using a two tailed t test for a mean The farmer picks one randomly selected tomato each from 50 randomly selected plants and uses a germination experiment to determine how many seeds from each tomato are viable She calculates the sample mean as 15 viable seeds per tomato with a standard deviation of 4 3 seeds Her sample data appear normal and do not contain any outliers Select the appropriate null and alternative hypotheses for Elizabeth s question Ho H

Suppose a fast food company claims that its kids meal has an average of 500 Cal with a standard deviation of 11 Cal Heather decides to test this claim believing that the average number of calories in a kids meal is greater than the company s laim She takes a random sample of 42 kids meals and finds that the mean number of Calories in these 42 meals is 509 Cal Select the appropriate null and alternative hypotheses for a population mean z test Ho H

Suppose that in the town of Springfield RI the number of days per year with no measurable precipitation is approximately normally distributed with a mean of 79 2 days and a standard deviation of 6 3 days Ms Johnson who lives on a farm just outside of Springfield wonders if the mean number of days with no measurable precipitation on her farm is different from in town Her grandfather maintained meticulous weather records She obtains a simple random sample of six years from her grandfather s records and determines that the mean number of days with no measurable precipitation in those years was 78 7 days She plans to conduct a one sample z test assuming that the standard deviation of days with no measurable precipitation is the same at the farm as in town Choose the appropriate null and alternative hypotheses for such a test Ho H

3 d ketch r c cos 20 Show your work b Find the slope of the tangent line to r cos 20 at 0 at 6 c Find the equation of the tangent line to polar A r cos 20

A sample of 276 people is surveyed The people are classified according to political affiliation Democrat Republican or Independent They are also classified according to opinion on a bill in favor of opposed to or indifferent to The results are given in the contingency table below Democrat Republican Independent In favor of Opposed to 24 48 21 35 49 20 Indifferent to 20 22 37 What is the relative frequency of respondents who are in favor of the bill Round your answer to two decimal places

A sample of 377 students at a university is surveyed The students are classified according to gender female or male They are also classified according to major biology business engineering mathematics or computer science The results are given in the contingency table below Biology Business Engineering Mathematics Computer science Female Male 37 41 46 40 20 43 49 20 49 32 Among all the students in the sample what is the relative frequency of male biology majors Round your answer to two decimal places A 2

Suppose that wedding costs in the Caribbean are normally distributed with a mean of 8000 and a standard deviation of 915 Using the Empirical rule below estimate the percentage of Caribbean weddings that cost You do not need to round your values a between 7085 and 8915 b above 8915 c below 5255 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 05 0 00 d between 5255 and 8915 Probability Density 2 35 Normal Distribution 13 5 0 15 40 30 20 0 34 34 13 5 2 35 0 15 H H 0 20 30 11 4

Which of the following statements are TRUE about the Normal Distribution Check all that apply The mean median and mode are all equal and occur at the center of the distribution Data values farther from the mean are less common than data values closer to the mean 50 of the data values lie at or above the mean The graph of the Normal Distribution is bell shaped with tapering tails that never actually touch the horizontal axis Data values are spread evenly around the mean About 95 of all data values lie within 1 standard deviation of the mean O The distribution is symmetric with a single peak

For a standard normal distribution find P Z 0 75 Round your probabilty accurate to 4 decimal places

Approximately 7 1 of residents in the Charleston area use public transportation on a regular basis If 39 residents are randomly selected what is the probability that exactly five of them use public transportation on a regular basis Round your answer to at least three decimals

An epidemiologist Epidemiologists are public health professionals who investigate patterns and causes of disease and injury in humans plans to conduct a survey to estimate the percentage of women who give birth How many women must be surveyed in order to be 99 confident that the estimated percentage is in error by no more than two percentage points Assume that a prior study conducted by the US Census Bureau showed that 82 of women give birth Please write down the formula used No complete sentence is necessary for this answer but please include units

According to the Rule of Three when we have a sam

Isabel has a bag with 8 balls numbered 1 through 8 She is play This game is this Isabel chooses one ball from the bag at rando is selected 4 if the number 4 is selected and 5 if the numbe If necessary consult a list of formulas

Assume that the Poisson distribution applies and that the m a Find the probability that in a year there will be 5 hurrican

A cooler contains 100 ice cream bars There are 30 Vanilla bars 40 Mint Chocolate Chip bars 10 Strawberry bars and 20 Rocky Road bars If one bar is randomly selected determine the probability that the bar selected is not Mint Chocolate Chip The probability that the bar selected is not Mint Chocolate Chip is Type an integer or a simplified fraction

Iker is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below Brightness Level x Hours y 10 Hours 8 7 6 S 43 2 1 O 10 85 90 97 97 5 3 2 8 2 5 1 4 2 3 20 30 40 50 60 70 80 Brightness Level What is the residual for the point 45 6 Round to 4 decimal places 29 29 45 46 6 7 5 7 6 90 100 11

It was asked to find a 90 confidence interval fo n a random sample of size n 87 Which of the 34 that are correct here is a 90 chance that the proportion of note 11 and 0 34 e proprtion of all students who take notes is be ith 90 confidence the proportion of all studen ith 90 confidence a randomly selected studen tween 0 11 and 0 34 here is a 90 chance that the proportion of the Help Post to forum

Given the following CPI table 1 Calculate the Net Inflation rate from 1983 to 1993 2 What is 20 of the net inflation rate from 1985 to 1986 3 What percent of the net inflation rate from 1977 to 1978 is 0 02 4 In 1980 the minimum wage was 3 10 in the US Use the CPI table to estimate the minimum wage in 1987 Year 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 CPI 60 6 65 2 72 6 82 4 90 9 96 5 99 6 104 9 107 6 109 6 113 6 118 3 124 0 130 7 136 2 140 3 144 5

heel has equally sized slices numbered from 1 ne are grey and some are white slices numbered 2 3 4 5 and 7 are grey slices numbered 1 6 and 8 are white wheel is spun and stops on a slice at random x be the event that the wheel stops on a white e and let P x be the probability of x not x be the event that the wheel stops on a e that is not white and let P not X be the bability of not X Event X For each event in the table check the outcome s that are contained in the event Then in the last column enter the probability of the event not X 1 1 2 3 4 5 6 78 O 0 0 0 Subtract C 1 P not X Outcomes P not V C O O O 010 Probability 0000 P not X Select the answer that makes the sentence true P X Cha 7 6 8 1 54 23

The amount of com chips dispensed into a 16 ounce bag by a dispensing machine has been identified as possessing a normal distribution with a mean of 16 5 ounces and a standard deviation of 0 2 ounce What chip amount represents the 67th percentile for the bag weight distribution Round to two decimal places OA 16 63 oz OB 16 09 oz OC 16 13 oz OD 16 59 oz

For a standard normal curve find the z score that separates the bottom 70 from the top 30 Round to two decima places OA 0 98 OB 0 52 OC 0 12 OD 0 48

Five balls numbered from 1 to s are placed into a bag Some are grey and some are white The balls numbered 2 4 and s are grey The balls numbered 1 and 3 are white A ball is selected at random Let x be the event that the selected ball is white and let P x be the probability of x Let not x be the event that the selected ball is not white and let P not X be the probability of not X a For each event in the table check the outcome s that are contained in the event Then in the last column enter the probability of the event Event X Outcomes 12345 U O U U U Probability b Subtract 1 P X P X not X 00000 P not X 010 X 00 3 X 5 12345 c Select the answer that makes the sentence true

A coin is tossed three times An outcome is represented by a string of the sort HTT meaning a head on the first toss followed by two tails The 8 outcomes are listed in the table below Note that each outcome has the same probability For each of the three events in the table check the outcome s that are contained in the event Then in the last column enter the probability of the event Event A Exactly one head Event B A tail on the first toss or the third toss or both Event C No tails on the first two tosses HTT TTH HTH HHT THT HHH THH TTT 0 0 O 0 O Outcomes O 0 O O 0 0 O O 0 Probability 0

The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 4 5 to 6 5 millimeters What is the probability that a randomly selected ball bearing has a diameter greater than 5 6 millimeters Round to four decimal places OA 0 8615 OB 0 4500 C 2 5000 OD 0 5091 www

The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6 5 minutes and a standard deviation of 1 minute Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6 minutes Round to four decimal places OA 0 3085 B 0 1915 C 0 3551 D 0 2674

A tile is selected from seven tiles each labeled with a different letter from the first seven letters of the alphabet The letter selected will be recorded as the outcome Consider the following events Event X The letter selected comes before D Event Y The letter selected is found in the word CAGE Give the outcomes for each of the following events If there is more than one element in the set separate them with commas 0 b Event X or Y a Event X and Y c The complement of the event Y 0 0 X S

1 30 pts Consider a to be a random va function pdf f x shown in Fig 1 a Find the value of a for f x to be b Compute the expected value and t x

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4 1 years and a standard deviation of 0 6 years He then randomly selects records on 54 laptops sold in the past and finds that the mean replacement time is 3 8 years Assuming that the laptop replacement times have a mean of 4 1 years and a standard deviation of 0 6 years find the probability that 54 randomly selected laptops will have a mean replacement time of 3 8 years or less P M 3 8 years Enter your answer as a number accurate to 4 decimal places Based on the result above does it appear that the computer store has been given laptops of lower than average quality Yes The probability of this data is unlikely to have occurred by chance alone O No The probability of obtaining this data is high enough to have been a chance occurrence

Raven invested some money in an account The balance in the account is given by the equation B 7900 120t where t is the number of years since the initial investment was made and B is the account balance The equation tells us that Raven started with account is Select an answer at a rate of in the account and that the balance in the Select an answer

Question 3 Suppose the amount of time it takes a Capt Rig announcement to touch down is uniformly distri a Find the probability that for a randomly sele the plane after the announcement Round to 1 b What is the longest landing time included in

d 7 Quiz for K Ques Find the critical value s for the Ho 20 0 05 n 15

d 7 Quiz for K Question 6 of Use the calculator displays to the right to m reject the null hypothesis at a significance l

Quiz for Ques For which confidence interval fo

17 Quiz for K Questic The statement represents a claim 9 9

low s your new car The General Social Survey reported that 92 of people who bought a car in the past five years were satisfied with their purchas low large a sample of car buyers needs to be drawn so that the sample proportion p who are satisfied is approximately normally distributed The sample size must be at least 63 X 5

Find the Z scores that separate the middle 89 of the distribution from the area in the tails of the standard normal distribution Click the icon to view a table of areas under the normal curve The Z scores are Use a comma to separate answers as needed Round to two decimal places as needed

2 0 and c Z 0 16 and Z 0 75 Click the icon to view a table of areas under the normal curve normal curve that lies between a Z 0 87 and Z 0 www a The area that lies between Z 0 87 and Z 0 87 is 0 6157 Round to four decimal places as needed b The area that lies between Z 2 21 and Z 0 is Round to four decimal places as needed

Assume the random variable X is normally distributed with mean 50 and standard deviation o 7 Compute the probability Be sure to draw a normal curve with the area corresponding to the probability shaded P 52 x 68 Click the icon to view a table of areas under the normal curve Which of the following normal curves corresponds to P 52 x 68 O A B Q Q Q O C 27

4 Empirical Tegan and Sara are working at a ticket stand at a carnival Over the past five hours they have kept track of the features of the last 100 people who have stopped by see table They have decided to spice up the rest of the day and have developed a game to play described from Tegan s perspective If the next person that stops by has short hair or glasses Tegan gets 12 points If the person is bald and not wearing glasses Tegan gets 120 points Otherwise Tegan loses 8 points the cost to play Using the provided data and empirical probabilities find the expected value for the game for Tegan Is the game a fair game If not find a fair price Hair Length Short Long Bald Glasses 14 11 17 No Glasses 21 32 5