Probability Questions and Answers

Question 26 of 32 worth 4 points points Express all answers as decimals a If you roll an 10 sided die yes they do exist the probability of rolling a 7 is b If you roll an 10 sided die the probability of rolling at least 7 is c The probability of choosing two hearts from a standard 52 card deck with replacement is d The probabilit Save

In which of the following situations is using a combination the appropriate counting technique A Counting the possibilities for a 1st 2nd and 3rd place winner in an upcoming Yu Gi Oh card tournament OB Counting ways you can choose 5 of your 125 light sabers C Counting the number of license plates are possible D Counting the number of 4 digit iPhone passcodes are possible assuming a code like 0000 is allowed OE None of the above Review

Question 8 of 32 worth 2 points In hypothesis testing it is possible to reject the null hypothesis but accept the claim True False Review Chosl

a Construct a scatterplot of the weight y versus the height x Weight pounds 240 235 230 225 Question Attempt 1 of 3 215

The price of milk would differ by 4 Correct Answer The price of milk would differ by 0 09 Part 2 3 Part 3 of 3 Predict the price of milk in a month when the price of eggs is 1 19 Round the answer to two decimal places

b Compute the correlation coefficient between the height and weight of the quarterbacks Round the answer to at least three decimal places The correlation coefficient is r 0 6995 Part 2 4 Part 3 of 4 c If a quarterback is below average in height would you expect him to be above average or below average in weight Explain I would expect the quarterback to be Choose one average in weight since r is Choose one

A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C and another bottle contains a label stating that it contains Merck pills with 40 mg of lisinopril that is used to treat high blood pressure Identify which one of the following errors is most serious explain why it is most serious and characterize the error as being a type I error or a type Il error 1 For lisinopril fail to reject Ho 40 mg when the mean is actually different from 40 mg ii For lisinopril reject Ho 40 mg when the mean is actually equal to 40 mg ili For vitamin C fail to reject Ho 500 mg when the mean is actually different from 500 mg iv For vitamin C reject Ho 500 mg when the mean is actually equal to 500 mg Error is most serious since this error is the most likely to result in a person GIED This error would be a type error

What does the notation zu indicate Za The expression 7 denotes the z score with an area of g

When randomly selecting an adult A denotes the event of selecting someone with blue eyes What do P A and P A represent P A represents the P A represents the

In a horse race a particular bet is won if you selected the three horses that finish first second and third and they can be selected in any order A certain horse race had a field of 16 horses What is the probability of winning this bet if you randomly select the horses The possibility of winning this bet when randomly selecting the horses is Round to five decimal places as needed

Find the probability that when a couple has three children at least one of them is a girl Assume that boys and girls are equally likely The probability is that at least one of the three children is a girl Simplify your answer Do not round

The article Effects of Bottle Closure Type on Consumer Perception of Wine Quality reported that in a sample of 106 wine consumers 22 thought that screw tops were an acceptable substitute for natural corks Suppose a particular winery decided to use screw tops for one of its wines unless there was strong evidence to suggest that fewer than 26 of wine consumers found this acceptable USE SALT a Using a significance level of 0 10 what would you recommend to the winery State the appropriate null and alternative hypotheses Ho P 0 26 H P 0 26 Ho P 0 26 H P 0 26 Ho p 0 26 H P 0 26 Ho P 0 26 H P 0 26 Ho P 0 26 H p 0 26 Calculate the test statistic and determine the P value Round your test statistic to two decimal places and your P value to four decimal places Z P value State the conclusion in the problem context

Yes Correct Answer No the x values must be positive Part 2 4 the x values must be positive Part 3 of 4 If the systolic pressures of two patients differ by 7 millimeters by how much would you predict their diastolic pressures to differ Round the answ three decimal places The diastolic pressure would differ by millimeters X S

7 Determine whether the association between the two variables is positive or negative The diameter of an apple and its weight The association between the diameter of an apple and its weight is Choose one positive negatius 8 X 9 10

5 6 Determine whether the association between the two variables is positive or negative The age of a car and the number of miles on its odometer 8 9 The association between age of a car and the number of miles on its odometer is Choose one 10 11 12

Given the probability distribution table below find the value of k X P x 6 0 15 12 0 30 24 36 0 25

An Internet research company surveyed 90 online shoppers each of whom made one purchase today The company recorded the type of purchase each shopper made Here is a summary Type of purchase Toys Electronics Beauty supplies Pet supplies Number of shoppers 28 19 0 25 18 Three shoppers from the survey are selected at random one at a time without replacement What is the probability that none of the three shoppers purchased toys Do not round your intermediate computations Round your final answer to three decimal places If necessary consult a list of formulas X S

Lisa conducted an experiment with two cards randomly chosen from a computer program There were 48 cards four colors of cards numbering 1 12 in each color She counted all cards 10 and above as 10 and all other cards at number value Lisa added the numbers and recorded the sums by separating them into groups of greater than or equal to 12 or less than 12 She also recorded whether the cards had the same value What is the experimental probability of receiving two cards with a sum less than 12 and with two cards that have the same value 01 12 04 0 O O 14 Pair 212 1 2 Yes No Same Value No 2 No 3 Yes No 4 No 5 Yes Yes Yes 6 No No 7 No No 8 Yes Yes 9 No No 10 No No 11 Yes Yes 12 No No

Determine if there are outliers in the data set State the outliers if they exist 709 699 700 830 697 685 10 517 612 214

Ho 1 0 OH H1 H 0 Ho Hi Hyo H H H O At 0 10 can it be concluded that the mean of the Eastern Conference is higher than the mean on the Western Conference based on these data a Which are the null and alternative hypotheses 10 12 Only need help with part c d and G M H 1 00 22 Eastern Conference X b What are the sample means and sample standard deviations Round each to 2 decimal places 65 73 1 20 Western Conference 77 59 72 58 37 57 66 55 61 X 83 60 75 58 78 59 70 58 62 61 59 211 38 c What is the test statistic Round to 2 decimal places 0 1225 e Which is the decision d What is the p value Round to 4 decimal places Fall to reject the null hypothesis Reject the null hypothesis f What is the reasoning for the decision There is enough evidence to conclude that the mean of the Eastern Conference is more than the mean of the Western Conference highest scorers There is not enough evidence to conclude that the mean of the Eastern Conference is more than the mean of the Western Conference highest scorers There is enough evidence to conclude that the mean of the Eastern Conference is the same as the mean of the Western Conference highest scorers There is not enough evidence to conclude that the mean of the Eastern Conference is the same as the mean of the Western Conference highest t

The Bureau of the Census reports the average commuting time for citizens of both Baltimore Maryland and Miami Florida To see if their commuting times appear to be any different in the winter random samples of drivers were surveyed in each city and the average commuting time for the month of January was calculated for both cities The results are provided below Sample size Sample mean min Population Standard Deviation Hoi HH2 ng i O O H1 H1 H 0 Hoi Hn Hz 0 O H1 H1 H 0 At the 0 06 level of significance can it be concluded that the commuting times are different in the winter a Which are the null and alternative hypotheses Ho H1 H2 0 H H1 H O Hoi Hi H2 0 OH H1 H 0 Miami X 4 40 31 2 7 2 b What is the test statistic Round to 2 decimal places c What is the p value Round to 4 decimal places Baltimore X 35 28 5 9 1

9 Given the graph of the distribution of fouls received by each player on a basketball team Frequency 1 2 3 4 5 3 5 53 3 2 5 52 2 1 6 0 5 2 3 3 0 2 Distibution of Fouls 3 Number of Fouls a Determine if the distribution represents one or two variable data 1 mark b Formulate two questions about the set of data 2 marks 5

In a large state 5 individuals are infected with Corona virus Suppose a particular test used for detecting the corona virus detects the virus 93 of the time i e if someone has corona virus the test detects it 93 of the time the remaining 7 of the time the test gives false negative But the test also gives a false positive 3 of the time Suppose a randomly selected individual tests positive for the Corona virus Given this test result what is the probability that the individual is actually infected with corona virus 0 075 0 21 0 93 03 7 0 62 0 90 0 58

Among a group of twenty students eight have been to Mexico and six have been to Canada Three students have been to both countries What is the probability that a student from this group went to Mexico or Canada O 8 8 8 07 O 0

3 Using the Table Below find the following Probabilities All of these people are in a room together and you randomly pick one person in the room via lottery Male Female Firefighter 9 8 Policemen 14 5 EMT 3 11 a What is the probability that the randomly chosen person is a female EMT b What is the probability that the chosen person is a Firefighter c What is the probability that the chosen person is either a male or a Policemen

1 If I have 3 types of Bread Wheat Rye and White 2 types of Proteins Chicken and Beef and 2 types of cheese American and Swiss Draw a graph that depicts all the unique sandwiches can you make

2 You Flip 3 fair coins a What is the Probability that all coins will land on heads b What is the Probability that 2 of the coins are heads and one is tai Think carefully

Which survey question has the least amount of bias Why are vegetables good for you How many hours of sleep do you get Do you think the media has a negative role in politics Why are teen drivers dangerous

Watch help video At a customer service call center for a large company the number of calls received per hour is normally distributed with a mean of 180 calls and a standard deviation of 15 calls What is the probability that during a given hour of the day there will be between 143 calls and 185 calls to the nearest thousandth

11 10 points A person makes monthly deposits of 100 at the end of each month for 40 years The annual interest rate is 5 How much money will she have at the end of 40 years for retirement Give your answer to the nearest dollar

Unit 7 Quiz 2 Review 1 Is the distribution a valid probability distribution Write yes or no 3 Number LARGE ZADE Probability a b 1 2 A die is loaded in such a way that the probabilities of getting 1 2 3 4 5 and 6 are 1 12 1 6 1 3 6 1 12 and 1 6 respectively Fill in the probability distribution 3 Name 4 X 5 1 2 3 4 5 P X 0 11 0 25 0 4 0 13 0 31 What is the probability that a 2 or greater is shown on the loaded die 6 What is the probability that a number less than 4 is shown on the loaded die 4 You roll a 12 sided die with numbers 1 12 What is the probability of rolling an odd number You roll a 12 sided die with numbers 1 12 What is the probability of rolling a number no more than 6 You roll a 12 sided die with numbers 1 12 What is the probability of rolling a number greater than 2 Unit 7 Quiz 2 Review Name 7 A player tosses two coins into the air He wins 1 dollar for the number of heads he will get However he will lose 5 dollars if neither coin is a head Calculate the expected value of this game and determine whether it is favorable for the player 8 You are at the fair playing a game where a ball is randomly hidden under one of 3 cups It costs 4 to play If you choose the cup with the ball under it you win back your money plus an additional 5 What is the expected value of this game 9 Sandra is playing a game There are 8 marbles in a bag 1 purple and 7 orange If she chooses the purple marble she will win 40 If she chooses the orange marble she will win 4 What is the expected value of Sandra s winnings from the game 10 An agent sells life insurance policies to six equally aged healthy people According to recent data the probability of a person living in these conditions for 30 years or more is 70 Is this a binomial experiment List all reasons why it is

This question 6 point s possible Below are the jersey numbers of 11 players randomly selected from a football team Find the range variance and standard deviation for the given sample data What do the results tell 45 69 9 24 5 38 55 76 44 2 20 Range Round to one decimal place as needed Sample standard deviation Sample variance Round to one decimal place as needed What do the results tell us Round to one decimal place as needed E OA Jersey numbers on a football team do not vary as much as expected OB Jersey numbers on a football team vary much more than expected OC The sample standard deviation is too large in comparison to the range O D Jersey numbers are nominal data that are just replacements for names so the resulting statistics are meaningless

This question 3 point s possible A study was conducted to determine how people get jobs The table lists data from 400 randomly selected subjects Construct a Pareto chart that corresponds Job Sources to the given data If someone would like to get a job what seems to be the most effective approach Choose the correct Pareto chart O A 300 250 200 150 100 50 0 HENM OB 300 250 200 150 100 50 0 OA Executive search firms E OB Networking N OC Mass mailing M O D Help wanted ads H EHMN If someone would like to get a job what seems to be the most effective approach O C 300 250 200 150 100 50 0 EHMN O D 300 250 200 150 100 50 0 Frequency 59 Executive search firms E 270 Help wanted ads H 30 Networking N Mass mailing M 41 HENM

What type of sampling is used Identify which of these types of sampling is used random systematic convenience stratified or cluster K To determine her power usage Miranda divides up her day into three parts morning afternoon and evening She then measures her power usage at 4 randomly selected times during each part of the day O O O O O Cluster Convenience Systematic Random This question 3 point s possible Stratified test

Determine whether this table represents a probability distribution X 0 1 2 3 P x 0 1 0 3 0 1 0 55 O No it is not a probability distribution O Yes it is a probability distribution

a The percentage of normal and healthy persons considered to have a fever is Round to two decimal places as needed Points 0 of 4 Assume that human body temperatures are normally distributed with a mean of 98 19 F and a standard deviation of 0 64 F a A hospital uses 100 6 F as the lowest temperature considered to be a fever What percentage of normal and healthy persons would be considered to have a fever Does this percentage suggest that a cutoff of 100 6 F is appropriate b Physicians want to select a minimum temperature for requiring further medical tests What should that temperature be if we want only 5 0 of healthy people to exceed it Such a result is a false positive meaning that the test result is positive but the subject is not really sick Click to view page 1 of the table Click to view page 2 of the table Save

Points 0 of 4 a The percentage of women who meet the height requirement is Round to two decimal places as needed Sav A survey found that women s heights are normally distributed with mean 63 5 in and standard deviation 2 5 in A branch of the military requires women s heights to be between 58 in and 80 in a Find the percentage of women meeting the height requirement Are many women being denied the opportunity to join this branch of the military because they are too short or too tall b If this branch of the military changes the height requirements so that all women are eligible except the shortest 1 and the tallest 2 what are the new height requirements Click to view page 1 of the table Click to view page 2 of the table

K Question 3 6 1 11 T The area of the shaded region is Round to four decimal places as needed HW Score 0 0 of 30 points O Points 0 of 2 Find the area of the shaded region The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 Z 0 86 Z 1 28 Sav

State your decision to the significance test in terms of the null hypothesis Consumer data reports that 50 of shoppers who enter a store on Black Friday end up making a purchase In order to receive a bonus for their efforts the marketing department of an electronics retailer must show that their stores have exceeded this proportion A random sample of 320 Black Friday customers found that 176 of them ending up making a purchase Use the following results and a 0 01 significance level to state your decision about Ho Ho p 0 50 0 H p 0 50 Test statistic z 1 79 p value 0 0368 W There is not enough information Reject Ho Reject H

There is a positive correlation between an individual s level of education and their annual income Therefore it can be concluded that nothing can be concluded from a positive correlation individuals earn more because they have higher levels of education individuals have higher annual incomes because they have attained higher levels of education higher annual incomes are the result of higher levels of education individuals with higher levels of education tend to have higher annual incomes

Conduct the appropriate hypothesis test and compute the test statistic It is claimed that the proportion of doctors who recommend the leading brand of ibuprofen is 90 To test this claim against the alternative that the actual proportion of doctors who recommend the leading brand is greater than 90 a random sample of 100 doctors results in 94 who indicate that they recommend the leading brand Compute the test statistic 1 33 1 67 1 67 1 33

April May June July August September October November December Send data to Excel Part 0 2 28 33 34 43 Can you conclude that false alarms are not equally likely to occur in any month Use the a 0 01 level of significanc Part 1 of 2 38 29 44 34 45 a Find the P value Use Excel round to four decimal places

The probability distribution of X the number of males with tinnitus ringing ears among 6 randomly selected males is as follows 0 aN P X a 0 57 1 exactly 4 0 25 2 0 1 3 0 03 b P X 2 or X 3 c P X 0 4 0 03 5 1 Use the random variable notation to express symbolically each of the following An event in which the number of males with tinnitus is exactly 4 The probability of an event in which the number of males with tinnitus is 2 Use the above probability distribution table to find the following a P X 5 0 01 0 01 The probability of an event in which the number of males with tinnitus is exactly 4 is equal to 0 03 Round the answer to 2 decimals Total Round the answer to 2 decimals 1 Round the answer to 2 decimals

A randomly selected card from a standard 52 card deck is noted The card is then replaced the deck is shuffled and a second card is selected and noted What is the probability that both cards are Aces chance that two Aces are randomly selected with replacement There is a

A boy owns 1 pairs of pants 5 shirts 8 ties and 6 jackets How many different outfits can he wear to school if he must wear one of each item He can wear different outfits

X 0 1 2 3 P x 0 1 0 25 0 05 0 6 Find the mean of this probability distribution Round your answer to one decimal

The table contains the number of M M s of each color that were found in a case M M Distribution Blue 467 P blue P brown P green P orange P red Brown 390 Find the probability of choosing each color based on this experiment Round to four decimal places if necessary P yellow Green 387 Orange 409 Red 435 Yellow 494 Total 2582

4 28 See Saw The table gives data on the heights above ground of the left and right seats of a see saw in feet Assume the trend is linear calculate the correlation and explain what it shows Left 4 3 C Right 0 1

Find the producers surplus at a price level of p 67 for the price supply equation below p S x 10 0 1x 0 0003x The producers surplus is Round to the nearest integer as needed

A manufacturer guarantees a product for 1 year The lifespan of the product after it is sold is given by the probability density function below where t is time in months 0 012e 0 012 ift20 f t 0 otherwise What is the probability that a buyer chosen at random will have a product failure A During the warranty B During the second year after purchase A What is the probability that the product will fail within one year Round to three decimal places as needed