Probability Questions and Answers

Which of the following is a property of binomial distributions O The sum of the probabilities of successes and failures is always 1 O All trials are dependent O The expected value is equal to the number of successes in the experiment O There are exactly three possible outcomes for each trial

1 The sample mean of observations x x2 Xn is given by 2 Sample median x 1 1 th ordered values average of 2 th and 1 th ordered values 3 Sample variance s x x Ex7 Ex or n 1 n 1 Ex 11 Number of outcomes containing A Total number of outcomes in the sample space when n is odd 4 Fourth spread Interquartile range fs upper fourth lower fourth 5 Any observation farther than 1 5f from the closest fourth is an outlier An outlier is extreme if it is more than 3f from the nearest fourth and it is mild otherwise P ANB P B when n is even 6 Let denote the null event When An B A and B are said to be mutually exclusive or disjoint events 7 P A UB P A P B P A n B 8 P A 1 P A 9 P A UA P S 1 10 P A N A N 11 Combination n k n k 12 Conditional probability of A given B P A B 13 The multiplication rule P A n B P A B P B

Using the Venn Diagram below what is the conditional probability of event B occurring assuming event A has happened P BIA O 0 77 O 0 63 0 41 0 24 A 0 24 0 41 0 23 B 0 12

Jake tosses a coin and rolls a six sided die All of the following are possible outcomes EXCEPT O Tails One O Tails Three O Heads Seven O Heads Five

O 0 42 O 0 22 O 0 60 A Using this Venn diagram what is the probability that event A or event B occurs 0 78 0 39 0 18 0 22 m 0 21

Which of the following statements is true for an outlier O It is a data point that is between Q1 1 5 x IQR and Q3 1 5 x IQR O It is a data point that is below Q1 1 5 x IQR or above Q3 1 5 x IQR O It is a data point that is below or above Q3 1 5 x IQR O It is a data point that is below or above Q1 1 5 x IQR

Which of the following statements is true O According to the Central Limit Theorem the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough O According to the Central Limit Theorem the mean of the sampling distribution is greater than the standard deviation O According to the Central Limit Theorem the mean of the sampling distribution is greater than the population mean O According to the Central Limit Theorem the mean of the sampling distribution is equal to the standard deviation

Which of the following statements is true O If the variance of a data set is 25 the standard deviation is 5 O If the variance of a data set is 25 the standard deviation is 12 5 OIf the variance of a data set is 25 the standard deviation is 50 If the variance of a data set is 25 the standard deviation is 625

Which of the following statements is true O A standard normal curve has a mean of 1 and a standard deviation of 2 O A standard normal curve has a mean of O and a standard deviation of 1 O A standard normal curve has a mean of 1 and a standard deviation of 1 O A standard normal curve has a mean of O and a standard deviation of 2

3 points The sample space when an octagonal Rubik s cube is rolled is S 1 2 3 4 5 6 7 8 Event A consists of odd numbers while event B consists of numbers that are at least 4 a 1 point Find the element s in AuB n A nB b 1 point Find the element s in A nB u A nB 05 0 1 point Find the element s in AnB n AnB

The manager of an amusement park conducts a survey among the people visiting the park to learn their favorite rides Out of 100 people randomly selected to complete the survey 25 people have chosen not to participate The manager s survey suffers from which of the following types of bias O Nonresponse bias O Response bias O Selection bias O There is no bias in the way this survey is carried out

In looking to determine the proportion of students who enjoy science which of the following might be a representative sample to take O 30 students who received high grades in their science class last semester O O O 30 students in the lunchroom 30 students who participated in the science fair 30 students who failed science class last year

A shoe retailer decides to record the styles and sizes of shoes that his customers choose He records this data for an entire year by keeping track of his customers purchases Which statement accurately describes the type of data the shoe retailer is collecting O The shoe retailer is gathering available data because customers tell him which shoe sizes and styles they prefer O The shoe retailer is gathering raw data because he is recording shoe sizes and styles by himself O The shoe retailer is receiving raw data on shoe sizes and styles from nearby shoe companies O The shoe retailer is receiving available data on shoe sizes and styles from nearby shoe companies

If n 210 and p p hat 0 82 find the margin of error at a 99 confidence level Give your answer to three decimals

A political candidate has asked you to conduct a poll to determine what percentage of people support her If the candidate only wants a 6 margin of error at a 99 confidence level what size of sample is needed Give your answer in whole people

Express the confidence interval 43 5 50 1 in the form of p ME

Express the confidence interval 33 5 46 7 in the form of p ME de

5 20 Waiting at an ER Part II Exercise 5 11 provides a 95 confidence interval for the mean waiting time at an emergency room ER of 128 minutes 147 minutes Answer the following questions based on this interval a A local newspaper claims that the average waiting time at this ER exceeds 3 hours Is this claim supported by the confidence interval Explain your reasoning b The Dean of Medicine at this hospital claims the average wait time is 2 2 hours Is this claim supported by the confidence interval Explain your reasoning c Without actly calculating the interval determine if the claim of the Dean from part b would be supported based on a 99 confidence interval

The cholesterol level of children is normally distributed 149 O a 63 O b 74 164 O c 26 179 194 199 209 If the average cholesterol level is 194 with a standard deviation of 15 what percentage of children have a cholesterol level lower than 199 Answers are rounded to the nearest whole percent 224 239

In a class of 250 students what is the mean variance and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution Answer choices rounded to the nearest whole number a Mean 54 Variance 8 Standard Deviation 62 b Mean 135 Variance 62 Standard Deviation 8 c Mean 53 Variance 62 Standard Deviation 8 d Mean 135 Variance 8 Standard Deviation 62

1 of 5 Find the expected

Let a be a normally distributed continuous randomariable with a mean of 63 and a standard deviation of 8 5 Determine the value of a such that the area to the left of x is 0 9931 Round the solution to two decimal places if necessary I

Determine the two values of z such that the middle 21 of the data lie between the two z values Round the solutions to two decimal places as z values are traditionally rounded The middle 21 of the data lie between z and z

The heights of all men in the United States are known to be normally distributed with a mean of 70 inches and standard deviation of 3 5 inches The U S Navy requires that fighter pilots have heights between 65 inches and 74 inches Find the percentage of men in the United States that meet this height requirement Round the solution to two decimal places if necessary P

Determine the value of z such that the area between 0 and z is 0 4554 and z is positive Round the solution to two decimal places as z values are traditionally rounded 2

Determine the following probabilities P z 1 51 P z 3 11 P z 5 78 P z 6 17 The above results are true because the probability that

Student loan debt is a growing problem in the United States According to Experian each student borrower owes an average of 31 400 The standard deviation of the amounts all student borrowers owe is 2 680 Determine the probability that a randomly selected student borrow owes between 22 425 and 29 249 in student loans Assume the distribution of all amounts owed by student borrows is normally distributed Round the solution to four decimal places if necessary P 22 425 x 29 249

Answer Number 5 Points 12 10 8 4 2 0 Mon Tue Animals Treated by Vet Wed Day Display Side by Side Bar Graph Step 2 of 2 On which day was the greatest total number of cats and dogs treated Thu Monday Tuesday Wednesday Thursday Friday Fri da ca

Find the area under the standard normal curve within two standard deviations of the mean Round the solution to four decimal places if necessary Area

The following bar graph represents the number of dogs and cats tre Number 10 D A 2 O Mon Tue Anima We

Consider the following frequency table representing the dist

Step 2 of 3 Determine the m Answer How to enter your answer

Question 13 2 points The elements for a valid contra a fair price

Given the following game calculate the expected value Two cards are chosen without replacement from a normal bridge deck If both the cards chosen are queens the player wins 50 If only one of the cards chosen is a queen the player wins 15 All other draws the player loses 1

In a city with three high schools all the ninth graders took a Standardized Test with these results Mean score on test Number of ninth graders High School Glenwood 76 90 69 253 315 157 Central City Lincoln High The city s PR manager who never took statistics claimed the mean score of all ninth graders in the city was 78 3 Of course that is incorrect What is the mean score for all ninth graders in the city Round to one decimal place mean of all ninth grader s scores

If you randomly select a letter from the phrase Ichiro Suzuki is at the top of the lineup what is the probability that you select a consonant Your answer must be in the form of a reduced fraction

What is misleading about both graphs Graph A Monthly Profits Profit 15 400 15 300 15 200 15 100 15 000 14 500 14 000 0 Oct Dec Jan Nov Feb Month Mar Profit There is nothing wrong on both graphs With a broken y axis it is hard to see the percent change The scale on the y axis is different between the two graphs The x axis is not scaled correctly The profits don t change at the same time on the graphs 17 000 16 500 16 000 15 500 15 000 14 500 14 000 0 Graph B Monthly Profits Oct Dec Nov Jan Feb Month Mar

2 Cond Prob Math XL LMS graded n the table to answer the question echnology class enrollment dependent or independent Expla rect choice below and fill in the answer box es within your ch answers

savvasrealize com assignments vi Lafayette High Sch C Infinite Camp 12 2 Cond Prob Math XL LMS grad e table to find the probability degree is not an associate s given that the

DOKI Age of Tax Filers of total DOK 2 30 00 15 00 DOK3 10 00 5 00 0 00 1 9 1 3 18 16 3 15 15 18 25 16 9 1 Which age group represents the highest percentage of taxpayers in 2020 18 2 28 34 2008 2020 18 ON 16 9 35 44 1845 DOKT 15 7 13 21 15 3 14 0 17 5 45 54 56 64 65 2 Which two age groups have seen the sharpest increase as a percentage of taxpayers from 2008 to 2020 3 Why do you think the percentage of tax filers has most dramatically increased for the 65 age group 4 What do you think causes the percent of filers to jump so dramatically between the under 18 group and the 18 25 group 5 What might have to happen in the U S for any dramatic changes to occur in future versions of this graph

uppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time If e leaves now and does not get stopped by any traffic lights he will arrive at work in exactly 8 minutes In between his house and his work there are three traffic lights A B and C Each light that stops him will cause him to arrive an additional 2 minutes later The following table displays the probability that he is stopped by each of the three traffic lights Assume that e probability that he is stopped by any given light is independent of the probability that he is stopped by any other light Traffic light A Traffic light B Traffic light C P A P B P C 0 8 0 1 0 4 What is the probability that the employee is not late for work Please write your answer in decimal form rounded to three Recimal places

K est What is the significance of the Choose the correct answer bel O A It gives information abo OB It is the expected value OS It can never be negative

You and a group of friends are going to a five day outdoor music festival during spring break You hope it does not rain during he festival but the weather forecast says there is a 10 chance of rain on the first day a 20 chance of rain on the second lay a 30 chance of rain on the third day a 35 chance of rain on the fourth day and a 40 chance of rain on the fifth day Assume these probabilities are independent of whether it rained on the previous day or not What is the probability that it does not rain during the entire festival Express your answer as a percentage to two decimal places

ty And Question 1 Sixty five percent of men consider the probability that exactly three of them

bability And 1 K Question 13 of 22 In a survey of U S adults with a sample size of 2046 World War II Two U S adults are selected at random through d

ability And Question 22 of 22 A frequency distribution is shown below Complete The number of televisions per household in a Televisions 0 2 Households 26 726 1 450

bability And T K Q Decide whether the rand x represents the number

ibility And K Question 5 of 22 Classify the following statement as an examp Explain your reasoning According to a survey the probability that an

bability And K Question 12 of The distribution of Master s degrees confe university is listed in the table Assume that a student majors in only one

bility uiz K Question 6 of 22 The access code for a gym locker consists of digit can be repeated Complete parts a thro a Find the number of possible access codes b What is the probability of randomly selectin c What is the probability of not selecting the