Probability Questions and Answers

Enter 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

Events 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

Events 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

Sara 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

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

Let 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

Table 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

Here 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

Events 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

Let 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

A 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

A 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

You 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

The 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

You 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

Before 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

You 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

According 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

Use 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

The 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

A 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

The 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

Steel 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

The 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

The 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

K 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

The 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

A 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

A 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

The 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

The 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

Suppose 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

A 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

An 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

An 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

SF S St

2 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

Suppose 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

A 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

Use 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

A 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

Assume 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

A 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

ten A group of data items and their mean are given Find a the deviation from the mean for each of the data items and b the sum of the deviations in part a 46 46 48 51 51 51 52 53 56 56 Mean 51 Oa 5 5 3 0 0 0 1 2 5 5 b 0 Oa 5 5 3 0 0 0 1 2 5 b 26 Oa 5 5 3 0 0 0 1 2 5 5 b 26 Oa 5 5 3 0 0 0 1 2 5 b 0

Probability of Compound Events Independent Events Dependent Events P A and B P A P B P A and B P A Mutually Exclusive Events Not Mutually Exclusive Events P A or B P A P B P A or B P A 01 26 5 1 3 0 getting red card and tails 3 52 13

In a study of 784 randomly selected medical malpra found that 495 of them were dropped or dismissed Use a 0 05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed Which of the following is the hypothesis test to be conducted O A OB Ho p 0 5 H p 0 5 Ho p 0 5 H p 0 5 O C Ho p 0 5 H p 0 5 O E Ho p 0 5 H p 0 5 OD Ho p 0 5 H p 0 5 OF Ho p0 5 H p 0 5

The overnight shipping business has skyrocketed in the last few years A study was conducted to study the customer satisfaction levels for one overnight shipping business In addition to the customer s satisfaction level the customers were asked how often they used overnight shipping The results are shown below in the following table What is the probability that a respondent did not have a high level of satisfaction with the company Round to the nearest hundredth Frequency of Use Less than 2 per month 2 5 per month Greater than 5 per month TOTAL 0 34 O 0 57 0 66 0 43 High Satisfaction 250 140 70 460 Medium Satisfaction 140 55 25 220 Low Satisfaction TOTAL 10 5 15 20 400 200 100 1700

A single six sided die is rolled twice The 36 equally likely outcomes are shown below Find the probability of getting two numbers whose sum is 5 Second Roll First Roll BB 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 HE 1 1 12 2 1 9 3 1 6

Form the negation of the statement Friday does not come before Saturday Choose the correct answer below OA Friday comes before Saturday B Saturday does come before Friday OC It is not true that Friday comes before Saturday D Sometimes Friday does not come before Saturday

1 point A newspaper conducted a statewide survey concerning the 1998 race for state senator The newspaper took a SRS of n 1100 registered voters and found that 570 would vote for the Republican candidate Let p represent the proportion of registered voters in the state who would vote for the Republican candidate We test a What is the z statistic for this test b What is the P value of the test this problem Ho p 50 Ha p 50