# Probability Questions and Answers

Statistics

ProbabilityThe probability statement was determined to be P z 0 14 Recall that the normal probability table gives the area under the curve to the left of a given z value An excerpt is given below Z 0 00 0 01 0 02 0 03 0 04 0 0 0 5000 0 5040 0 5080 0 5120 0 5160 0 05 0 06 0 07 0 1 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 2 0 5793 0 5832 0 5871 0 5910 0 08 0 5199 0 5239 0 5279 0 5319 0 09 0 5359 0 5675 0 5714 0 5753 0 5948 0 5987 0 6026 0 6064 0 6103 0 6141 Use the above table to find the probability of completing the exam in an hour or less P z 0 14 rounding the result to four decimal places P z 0 14

Statistics

ProbabilityThe correct size of a nickel is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each income group who drew the nickel too small and too large Low Income High Income Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from the low income group that drew the nickel too large is b The proportion of children from the high income group that drew the nickel too large is c The proportion of all children that drew the nickel too large is d If a child is picked at random what is the probability they are in the low income group given they drew the nickel too large e If a child is picked at random what is the probability they are in the high income group OR drew the

Statistics

ProbabilityThe correct size of a certain object is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each group who drew the certain object too small and too large Group 1 Group 2 Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from group 1 that drew the object too large is b The proportion of children from group 2 that drew the object too large is c The proportion of all children that drew the object too large is d If a child is picked at random what is the probability they are in group 1 given they drew the object too large e If a child is picked at random what is the probability they are in group 2 OR drew the object too large

Statistics

ProbabilityPhi Delta Kappa PDK is an international professional organization for educators that in collaboration with Gallup has been conducting polls on the public s attitudes toward the public schools since 1969 The following was one of the questions on the most recent poll conducted June 4 13 2011 Most teachers in the nation now belong to unions or associations that bargain over salaries working conditions and the like Has unionization in your opinion helped hurt or made no difference in the quality of public school education in the United States The respondents answers broken down by party affiliation is shown below Republican Democrat Independent Helped Hurt 35 197 52 6 Made no difference Don t know refused Which of the following statements is correct 146 78 105 12 69 178 90 4 O A histogram or a box plot would be useful to investigate if distribution of opinion on teachers belonging to unions or bargaining associations varies by political party affiliation O The results of the survey suggest a relationship between opinion on teachers belonging to unions or bargaining associations and political party affiliation O 14 of Republicans and 58 of Democrats think that teachers belonging to unions or bargaining associations helped the quality of public school education in the United States O The results of the survey suggest that opinion on teachers belonging to unions or bargaining associations and political party affiliation are independent

Statistics

ProbabilityEvery cereal box has a gift inside but you cannot tell from the outside what the gift is The store manager assures you that 13 of the 60 boxes on the shelf have the secret decoder ring The other 47 boxes on the shelf have a different gift inside If you randomly select two boxes of cereal from the shelf to purchase what is the probability that BOTH of them have the secret decoder ring Give answer as a decimal correct to four decimal places probability

Statistics

ProbabilityGiving a test to a group of students the grades and shirt colors are summarized below A B Red Shirt 19 3 Blue Shirt 14 2 C Total 35 33 68 13 17 Total 17 21 30 If one student is chosen at random a Find the probability that the student has a Red Shirt GIVEN they got a C Round to 4 decimal places if needed b Find the probability that the student got a C GIVEN they are wearing a Red Shirt Round to 4 decimal places if needed

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ProbabilityWrite the given number using prime factorization Write your answer using Exponential Notation For instance 98 2 7 2 Instructions Find the prime factorization of 6

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ProbabilityEnter the prime factorization of 77 Use exponents for repeated factors Be sure to use the between different factors For example the pr factorization for 12 can be entered as 2 2 3 or 3 2 2

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ProbabilityEvents A and B are independent if the occurrence of one does not affect the probability of the other occurring This statement is best represented in symbols by OP A B P A A B A OP A and B P A OA and B A

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ProbabilityEvents A and B are mutually exclusive if they can not occur simultaneously This statement is best represented in symbols by P A and B 0 A given B 0 A and B 0 P A B 0

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ProbabilitySara draws the 7 of hearts from a standard deck of 52 cards Without replacing the first card she then proceeds to draw a second card a Determine the probability that the second card is another 7 P 7 7 of hearts b Determine the probability that the second card is another heart P heart 7 of hearts c Determine the probability that the second card is a club P club 7 of hearts d Determine the probability that the second card is a 3 P 3 7 of hearts

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ProbabilityTwo dice are rolled What is the probability P sum is 3 OO 11 18 1 12 1 18 19 36

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ProbabilityLet P U 0 15 and P V 0 44 Events U and V are mutually exclusive Find P U or V O 0 59 O 0 29 O 2 9333333333333 O 0 066 O 0 29 O 0 34090909090909

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ProbabilityTable Frequencies by grades and shirt color Shirt Color A B Blue Shirt 20 10 Red Shirt Total C 4 7 3 11 27 13 15 Total 34 21 55 If one student is chosen at random from those who took the test Find the probability that the student was Red Shirt GIVEN they got an A

Statistics

ProbabilityHere is the probability model for the blood type of a randomly chosen person in the United States Blood type 0 A B AB Probability 0 49 0 17 0 03 0 31 What is the probability that a randomly chosen American does not have type O blood Round to the nearest 0 01

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ProbabilityEvents A and B are mutually exclusive if they can not occur simultaneously This statement is best represented in symbols by OA given B 0 OP A B 0 OP A and B 0 O A and B 0

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ProbabilityLet P U 0 3 and P V 0 34 Events U and V are mutually exclusive Find P U or V O 0 102 O 0 04 O 0 04 O 0 88235294117647 0 64 O 1 1333333333333

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ProbabilityA certain virus infects one in every 600 people A test used to detect the virus in a person is positive 90 of the time if the person has the virus and 10 of the time if the person does not have the virus Let A be the event the person is infected and B be the event the person tests positive a Find the probability that a person has the virus given that they have tested positive b Find the probability that a person does not have the virus given that they have tested negative

Statistics

ProbabilityA poll showed that 58 4 of Americans say they believe that Marilyn Monroe had an affair with JFK What is the probability of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK Round to 3 decimal places

Statistics

ProbabilityYou may need to use the appropriate appendix table to answer this question According to Money magazine Maryland had the highest median annual household income of any state in 2018 at 75 847 t Assume that annual household income in Maryland follows a norma distribution with a median of 75 847 and standard deviation of 33 800 a What is the probability that a household in Maryland has an annual income of 90 000 or more Round your answer to four decimal places b What is the probability that a household in Maryland has an annual income of 50 000 or less Round your answer to four decimal places c What is the probability that a household in Maryland has an annual income between 40 000 and 70 000 Round your answer to four decimal places d What is the annual income in of a household in the ninety first percentile of annual household income in Maryland Round your answer to the nearest cent

Statistics

ProbabilityThe average starting salary of this year s MBA students is 55 000 with a standard deviation of 5 000 Furthermore it is known that the starting salaries are normally distributed What are the minimum and the maximum starting salaries in dollars of the middle 95 of MBA graduates You may need to use the appropriate appendix table or technology to answer this question Round your answers to the nearest dollar minimum maximum

Statistics

ProbabilityYou may need to use the appropriate appendix table to answer this question The average return for large cap domestic stock funds over three years was 14 4 Assume the three year returns were normally distributed across funds with a standard deviation of a What is the probability an individual large cap domestic stock fund had a three year return of at least 23 Round your answer to four decimal places b What is the probability an individual large cap domestic stock fund had a three year return of 10 or less Round your answer to four decimal places c How big does the return have to be to put a domestic stock fund in the top 25 for the three year period Round your answer to two decimal places

Statistics

ProbabilityBefore finding this probability the random variable x needs to be converted to the normal random variable z so that a table of probabilities can be used Recall the formula to convert an x value to the normal random variable z where x is the value that needs to be converted u is the population mean and is the population standard deviation Z x x The mean was given to be 14 4 and the standard deviation was given to be 4 4 Find the value of the z statistic corresponding to x 16 rounding the result to two decimal places 4 4 6 Thus the new probability statement using the normal random variable z is P Z

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ProbabilityYou may need to use the appropriate appendix table or technology to answer this question Given that z is a standard normal random variable what is the value of z if the area to the left of z is 0 2546 O 0 66 0 60 0 60 0 66 Noor

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ProbabilityAccording to a survey 54 of the residents of a city oppose a downtown casino Of these 54 about 8 out of 10 strongly oppose the casino Complete parts a through c a Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino b Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino c Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino Explain a The probability that a randomly selected resident opposes the casino and strongly opposes the casino is Round to three decimal places as needed b The probability that a randomly selected resident who opposes the casino does not strongly opposes the casino is Round to three decimal places as needed c Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino Explain Choose the correct answer below A No this is not unusual because the probability is less than or equal to 0 05 B Yes this is unusual because the probability is less than or equal to 0 05 OC No this is not unusual because the probability is not less than or equal to 0 05 D Yes this is unusual because the probability is not less than or equal to 0 05

Statistics

ProbabilityUse the frequency distribution which shows the number of American voters in millions according to age to find the probability that a voter chosen at random is in the 18 to 20 years old age range The probability that a voter chosen at random is in the 18 to 20 years old age range is Round to three decimal places as needed Ages 18 to 20 21 to 24 25 to 34 35 to 44 45 to 64 65 and over Frequency 5 8 8 8 23 2 22 3 51 4 28 2

Statistics

ProbabilityThe probability distribution for the random variable x follows X 20 0 25 25 0 15 30 0 20 35 0 40 a Is this probability distribution valid Explain Since f x O for all values of x and f x b What is the probability that x 30 c What is the probability that x is less than or equal to 25 d What is the probability that x is greater than 30 this Select roper probability distribution is not

Statistics

ProbabilityA psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1 2 or 3 Let x be a random variable indicating the number of sessions rec the patient s trust The following probability function has been proposed for x 1 2 or 3 f x a Is this probability function valid Explain This probability distribution Select valid because Select for x 1 2 3 Also f x b What is the probability that it takes exactly 2 sessions to gain the patient s trust Round your answer to three decimal places c What is the probability that it takes at least 2 sessions to gain the patient s trust Round your answer to three decimal places

Statistics

ProbabilityThe lengths of a particular animal s pregnancies are approximately normally distributed with mean 276 days and standard deviation o 16 days a What proportion of pregnancies lasts more than 288 days b What proportion of pregnancies lasts between 264 and 284 days c What is the probability that a randomly selected pregnancy lasts no more than 244 days d A very preterm baby is one whose gestation period is less than 252 days Are very preterm babies unusual a The proportion of pregnancies that last more than 288 days is Round to four decimal places as needed b The proportion of pregnancies that last between 264 and 284 days is Round to four decimal places as needed c The probability that a randomly selected pregnancy lasts no more than 244 days is Round to four decimal places as needed d The probability of a very preterm baby is This event than 0 05 Round to four decimal places as needed unusual because the probability is

Statistics

ProbabilitySteel rods are manufactured with a mean length of 22 centimeter cm Because of variability in the manufacturing process the lengths of the rods are approximately normally distributed with a standard deviation of 0 07 cm Complete parts a to d RECID a What proportion of rods has a length less than 21 9 cm Round to four decimal places as needed

Statistics

ProbabilityThe time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution with a mean of 19 minutes and a standard deviation of 3 minutes a The automotive center guarantees customers that the service will take no longer than 20 minutes If it does take longer the customer will receive the service for half price What percent of customers receive the service for half price b If the automotive center does not want to give the discount to more than 5 of its customers how long should it make the guaranteed time limit www a The percent of customers that receive the service for half price is Round to two decimal places as needed

Statistics

ProbabilityThe mean incubation time for a type of fertilized egg kept at a certain temperature is 17 days Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days Complete parts a through e below a Draw a normal model that describes egg incubation times of these fertilized eggs Choose the correct graph below Click here to view graph b Click here to view graph a Click here to view graph c Click here to view graph d b Find and interpret the probability that a randomly selected fertilized egg hatches in less than 15 days The probability that a randomly selected fertilized egg hatches in less than 15 days is Round to four decimal places as needed

Statistics

ProbabilityK Frequency Click here to view the sample data Click here to view the table of critical values for normal probability plots a Draw a relative frequency histogram with lower class limit of the first class equal to 0 and class width 20 O A OB Frequency O C A data set represents the wait time in minutes for a random sample of 100 visitors to Disney s Dinosaur Ride in Animal Kingdom Technology was used to obtain a random sample of 40 observations from the original sample of 100 visitors Complete parts a through c below ONW 25 Wait Time in minutes at Dinosaur Ride 20 20 40 Wait Time Wait Time in minutes at Dinosaur Ride 40 Wait Time 60 60 80 80 Q Q Q G Frequency Frequency 30 25 3221 O D Wait Time in minutes at Dinosaur Ride 30 25 0 20 Wait Time in minutes at Dinosaur Ride 20 40 Wait Time 40 Wait Time b Comment on the shape of the distribution Choose the correct answer below A The distribution is bell shaped OB The distribution is skewed right QC The distribution is ckownd loft 60 8 9 60 80 80 G Q Q

Statistics

ProbabilityThe P value measures the strength of evidence O A sometimes against the null hypothesis and sometimes against the alternative hypothesi B the interpretation depends on whether we reject the null hypothesis O C against the alternative hypothesis D against the null hypothesis

Statistics

ProbabilityA veterinarian collects data on the number of times race horses are raced during their career The researcher finds the average number of races a horse enters is 15 3 with a standard deviation of s 6 8 in a sample of n 20 horses The standard error of the sample mean is given by rounded to three digits O A 1 560 OB 0 358 O C 0 340 O D 1 521

Statistics

ProbabilityA statistic is said to be unbiased if O A the person computing it doesn t favor any particular outcome B it is used for only honest purposes C the mean of its sampling distribution is equal to the true value of the parameter being estimated O D the person who calculated the statistic and the subjects whose responses make up the statistic were

Statistics

ProbabilityThe distribution of actual weights of 8 ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8 1 ounces and standard deviation 0 2 ounces A sample of 10 of these cheese wedges is selected The distribution of the sample mean of the weights of cheese wedges is O A approximately Normal mean 8 1 standard deviation 0 020 B approximately Normal mean 8 1 standard deviation 0 2 O C approximately Normal mean 8 1 standard deviation 0 063 O D It is not possible to tell because the sample size is too small

Statistics

ProbabilityThe incomes in a certain large population of college teachers have a Normal distribution with mean 75 000 and standard deviation 10 000 Sixteen teachers are selected at random from this population to serve on a committee What is the probability that their average salary is more than 77 500 OA 0 1587 OB 0 0228 OC 0 8413 O D essentially 0

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ProbabilitySuppose X is a random variable with the binomial distribution with n 4 and p 1 4 The probability X is greater than or equal to 1 is A 0 6836 B 0 3164 C 0 0039 O D 0 9961

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ProbabilityA college basketball player makes 5 6 of his free throws Assuming free throws are independent the probability that he makes exactly three of his next four free throws is O A 0 0 00 O B O C O D 00 O Q

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ProbabilityAn event A will occur with probability 0 5 An event B will occur with probability 0 6 The probability that both A and B will occur is 0 1 We may conclude that O A events A and B are independent O B events A and B are disjoint OC either A or B always occurs OD None of the answer choices is correct

Statistics

ProbabilityAn event A will occur with probability 0 5 An event B will occur with probability 0 6 The probability that both A and B will occur is 0 1 The conditional probability of B given A is OA 5 6 OB 1 5 O C 1 6 O D The answer cannot be determined from the information given

Statistics

Probability2 Sunn Company manufactures a single product that sells for 100 per unit and whose variable costs are 76 per unit The company s annual fixed costs are 338 400 ints eBook Hint Print References 1 Prepare a contribution margin income statement at the break even point 2 If the company s fixed costs increase by 126 000 what amount of sales in dollars is needed to break even Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare a contribution margin income statement at the break even point SUNN COMPANY Contribution Margin Income Statement at Break Even Amount Check m

Statistics

ProbabilitySuppose the lengths of human pregnancies are normally distributed with 266 days and a 16 days Complete parts a and b below BOCCH a The figure to the right represents the normal curve with 266 days and a 16 days The area to the left of X 240 is 0 0521 Provide two interpretations of this area Provide one interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals A The proportion of human pregnancies that last less than OB The proportion of human pregnancies that last more than days is days is OB The proportion of human pregnancies that last less than days is Provide a second interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals OA The probability that a randomly selected human pregnancy lasts less than OB The probability that a randomly selected human pregnancy lasts more than b The figure to the right represents the normal curve with 266 days and 16 days The area between x 285 and x 305 is 0 1101 Provide two interpretations of this area Provide one interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals Use ascending order OA The proportion of human pregnancies that last between and days is 240 266 or more than days is days is ON A 266 285 305 or more than Provide a second interpretation of the area using the given values Select the correct choice below and fill in the answer boxes to complete your choice Type integers or decimals Use ascending order OA The probability that a randomly selected human pregnancy lasts less than OB The probability that a randomly selected human pregnancy lasts between and days is ON days is

Statistics

ProbabilityA simple random sample of 10 pages from a dictionary is obtained The numbers of words defined on those pages are found with the results n 10 x 55 4 words s 16 2 words Given that this dictionary has 1436 pages with defined words the claim that there are more than 70 000 defined words is equivalent to the claim that the mean number of words per page is greater than 48 7 words Us a 0 01 significance level to test the claim that the mean number of words per page is greater than 48 7 words What does the result suggest about the claim that there are more than 70 000 defined words Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim Assume that the population is normally distributed What are the null and alternative hypotheses O A Ho H 48 7 words H 48 7 words C Ho H 48 7 words H 48 7 words Determine the test statistic Round to two decimal places as needed Determine the P value Round to three decimal places as needed State the final conclusion that addresses the original claim Ho There is evidence to support the claim that there CID OB Ho 48 7 words H 48 7 words O D Ho H 48 7 words H H 48 7 words 70 000 defined words in the dictionary

Statistics

ProbabilityUse the sample data and confidence level given below to complete parts a through d A drug is used to help prevent blood clots in certain patients In clinical trials among 4376 patients treated with the drug 139 developed the adverse reaction of nausea Construct a 95 confidence interval for the proportion of adverse reactions a Find the best point estimate of the population proportion p 0 032 Round to three decimal places as needed b Identify the value of the margin of error E E Round to three decimal places as needed c Construct the confidence interval p 0 Round to three decimal places as needed d Write a statement that correctly interprets the confidence interval Choose the correct answer below OA One has 95 confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion OB One has 95 confidence that the sample proportion is equal to the population proportion OC 95 of sample proportions will fall between the lower bound and the upper bound OD There is a 95 chance that the true value of the population proportion will fall hebwoon tha

Statistics

ProbabilityA genetic experiment with peas resulted in one sample of offspring that consisted of 449 green peas and 160 yellow peas a Construct a 90 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 90 confidence interval Express the percentages in decimal form p 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 O 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

Statistics

ProbabilityAssume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors Use the table below to find the minimum sample size needed to be 99 confident that the sample standard deviation s is within 1 of o Is this sample size practical 6 To be 95 confident that s is within of the value of o the sample size In should be at least To be 99 confident that s is within of the value of o the sample size In should be at least The minimum sample size needed is Is this sample size practical 1 5 10 20 30 40 50 OC Yes because 19 205 768 192 48 21 12 8 1 5 10 20 30 40 50 33 218 1 336 336 85 38 22 14 OA Yes because the sample size should be as large as possible for most applications OB No because the sample size is excessively large to be practical for most applications the sample size is small enough to be practical for most applications O D No because the sample size should be as small as possible for most applications

Statistics

ProbabilityA data set includes 106 body temperatures of healthy adult humans having a mean of 98 7 F and a standard deviation of 0 66 F Construct a 99 confidence interval estimate of the mean body temperature of all healthy humans What does the sample suggest about the use of 98 6 F as the mean body temperature Click here to view a t distribution table Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table What is the confidence interval estimate of the population mean F H F Round to three decimal places as needed What does this suggest about the use of 98 6 F as the mean body temperature A This suggests that the mean body temperature is lower than 98 6 F OB This suggests that the mean body temperature is higher than 98 6 F C This suggests that the moon h