Probability Questions and Answers

Evaluate the numerical expression 2 04 O NA

Find the mean of the following probability distribution X P x 0 0 2492 1 0 2492 2 0 2249 3 0 1184 4 0 1583 mean report answer rounded to one decimal place

A probability distribution for various prize values is given by the following table Probabilities Prizes 0 00 100 00 500 00 10 000 00 0 75 0 14 0 08 0 03 Find the expected value of a prize Round your answer to two decimal places Do not include a dollar sign in your answer It is already included at the left

You are playing a game where you draw a card from a standard deck and you will win 19 if you draw a face card 19 if you draw an ace and lose 18 if you draw any other card What is the expected gain from this game

Hamburgers can be purchased from two different popular fast food restaurants Restaurant A sells 11 burgers for 14 19 and Restaurant B sells 2 burgers for 2 64 Which restaurant offers the best value per hamburger and what is its amount Restaurant A for 1 29 O Restaurant B for 1 29 Restaurant A for 1 32 Restaurant B for 1 32

A retail clothing store offers customers an opportunity to open up a credit card during checkout One location of the retail clothing store states that the number of credit cards A that are opened t months since January can be modeled by the function A t 10 2t The number of credit cards opened at another location B is defined by the function B t 25 t What is an expression that can be used to determine the total amount of credit cards opened at the two locations O A B t 35 t O A B t 35 3t O AB t 15 t O AB t 15 3t

Mrs Burke s mathematics class has 102 students

84 and X na test for the difference between two proportions the sample sizes were n 119 and 80 and the numbers of events were X1 A test is made of the hypotheses Ho P P versus H P P2 Part 0 3 Part 1 of 3 a Compute the P value using your calculator Round your answer to four decimal places The P value is 0 0826 Part 1 3 Part 2 of 3 X S b Can you reject Ho at the a 0 05 level of significance

The Central Limit Theorer K An engineer is goin distributed weights Click here to view p Click here to view

The regression equation below relates the scores students in an advanced statistics course received for homework completed and for the subsequent midterm exam Homework scores are based on assignments that preceded the exam The maximum homework score a student could obtain was 600 and the maximum midterm score was 400 The regression line that was obtained is given by 9 84 4 0 91x If a student had a homework score of 508 the midterm score would be predicted to be rounded to an integer O 336 None of the answer options is correct 378 298

Does exposure to classical music through instrument lessons or concert attendance improve a child s scholastic performance In a study researchers measured the amount of exposure to classical music for a group of children along with their scores on the state s academic proficiency exam The response variable in this study is the child s score on the state s proficiency exam the type of instrument a child plays the amount of exposure a child has to classical music whether a child passed the state s proficiency exam O

The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force versus the number of juvenile violent crime arrests for each of the 50 states The least squares regression line has been drawn in on the plot 1600 O 1400 5 8 8 8 8 200 200 contingency extrapolation 6 10 Percent Not in School or Labor O causation 12 Predicting the number of juvenile violent crime arrests if 25 of the children are not in school or in the labor force is called correlation 14 16

5 points Frequent food questionnaires FFQ are a simple way to obtain information on the foods individuals consume by asking them questions about typical amounts of food consumed in a day a week or a month A more accurate picture is obtained by obtaining a detailed food diary DR for several days that are randomly chosen over a certain time period The data obtained from frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire The data below are for seven individuals who participated in such a study on alcohol consumption DR 8 26 0 83 15 13 15 10 11 16 7 49 5 12 12 84 1 76 0 22 66 25 06 The correlation for these data is 0 77 0 89 None of the answer options is correct 0 87 FFQ 1 68

John s parents recorded his height at various ages up to 66 months Below is a record of the results 48 Age months 36 54 60 66 38 41 45 Height inches 35 43 John s parents decide to use the least squares regression line of John s height on age to predict his height at age 21 years 252 months We conclude th such a prediction could be misleading because it involves extrapolation All of the answer options are correct John s height in inches should be about half his age in months John s parents will get a fairly accurate estimate of his height at age 21 years because the data are clearly correlated

Which of the following statements is correct A negative value for the correlation r indicates the data are strongly unassociated The correlation always has the same units as the y variable but not the x variable The correlation always has the same units as the x variable but not the y variable Changing the units of measurement of x or y does not change the value of the correlation r

5 points An economist conducted a study of the possible association between weekly income and weekly grocery expenditures Of particular interest was whether higher income would result in shoppers spending more on groceries A random sample of shoppers at a local supermarket was obtained A questionnaire was administered asking about the weekly income of each shopper s family and their grocery bill for that week The explanatory variable is weekly expenditure gender None of the answer options is correct weekly income

25 points In many fast food restaurants there is a strong correlation between a menu item s fat content measured in grams and its calorie content We want to investigate this relationship Using all of the food menu items at a well known fast food restaurant the fat content and calorie content were measured We decide to fit the least squares regression line to the data with fat content x as the explanatory variable and calorie content v as the response variable A scatterplot of the data with regression line included and a summary of the data are provided One of the menu items is a hamburger with 117 grams of fat and 1520 calories Care cos r 0 979 correlation between x and y 40 35 grams mean of the values of x 5 662 88 calories mean of the values of y 27 99 grams standard deviation of the values of x 324 90 calories standard deviation of the values of y Refer to the example data point 117 grams 1520 calories What is the residual corresponding to this observation 4 calories 10 calories 4 calories 14 calories

The probability distribution of the random variable X is shown in the accompanying table X P X x Find the following a P X 0 b P XS 3 c P 2 x 2 d P X 2 e P X 0 1 P X 1 5 0 18 3 0 12 2 0 0 33 0 17 2 0 10 3 0 10

1 How did the media impact and reflect gender roles of the 1950s and 60 s 2 Where do we see remnants of 1950s gender roles and gender expectations in modern society

The drug Oxycontin oxycodone is used to treat pain but it is dangerous because it is addictive and can be lethal In clinical trials 227 subjects were treated with Oxycontin and 52 of them developed nausea a Construct a 95 confidence interval estimate of the percentage of Oxycontin users who develop nausea b Compare the result from part a to this 95 confidence interval for 5 subjects who developed nausea among 45 subjects given a placebo instead of Oxycontin 1 93 p 20 3 What do you conclude the above problem please write out the work for each of the following steps Please note that you do not have to number these steps but your work hould correspond with them 1 Read the problem carefully to determine which type of analysis is being performed 2 Identify the parameter being estimated 3 Write down the formula s used 4 Determine the information needed to calculate E from the context of the problem 5 Substitute all the values into E to calculate E 6 Substitute E and pintop E p p E Round answer to three significant figures Write a summary sentence

webpage www mathsisfun com data quincunx html Before moving on get to know the simulator by playing with the features a bit Change the number of rows the probabilities and the speed of the marbles as they fall What do you notice about the way the marbles fall as you change the probabilities What exactly do these probabilities seem to describe

A man named George Cramer created a Crypto token called Gramer He realized that his token was trading for 0 13 a token in US crypto exchanges but 0 16 in Asian Crypto Exchange Every time Cramer sells or buys a token the Exchange charges him 0 01 How many tokens must Cramer sell to become a millionair

1 The numbers of cookies in a shipment of bags are normally distributed with a mean of 62 ans deviation of 4 What percent of bags of cookies will contain between 58 and 66 cookies 58 62 4

where marbles are dispensed into an array of pegs The pegs force the marbles to randomly change direction At the bottom of the board are bins to catch the marbles 0 1 2 3 4 5 6 7 When a falling marble strikes a peg it will either bounce left or right Galton s motivation was to study the final distribution of marbles amongst the bins 1 Consider a quincunx with only 3 rows of pegs a Draw this quincunx and label the bins starting with zero on the far left b How many bins does it have to catch the marbles c Count the number of different paths a marble could take to eventually land in bin 2 How many are there d How many different paths to land in bin 1 e How many paths to land in bin 0 f How many paths to land in bin 3

was 419 On the final exam the mean score of the sample was 56 3 and the sample standard deviation was 13 8 Solve the following questions 1 5 Question 3 What percentile multiplier would you use to construct the 95 confidence interval for the mean score of the whole STA 13 class Find one from the t table O 1 960 2 009 1 pts 1 684

In checking conditions for constructing confidence intervals for a population mean it s important to plot the distribution of sample data Below are dot plots describing samples from three different populations For which of the three samples would it be safe to construct a t interval Plot X 01 Select one 3 4 5 6 7 8 9 Plot Y 0123456789 a Plot Y only b Plot X only c Plots Y and Z d Plot Z only e None of the plots 2 1 Plot Z 0 1 2 3 4 5 6 7 8 9

Does room temperature affect cognitive function A psychologist randomly divides 60 volunteers into two groups One group of 30 solves a crossword puzzle in a room kept at 72 F the other group of 30 solves the puzzle in a room kept at 85 F The mean completion time x for the subjects in the cool room is 20 minutes and the standard deviation is S 6 minutes The mean x for the subjects in the warm room is 26 minute and the standard deviation is S2 8 minutes Let and 2 represent the mean completion times for all potential volunteers similar to the ones in this study when they are in cool or warm rooms respectively Using technology which of the following is a 99 confidence interval for Select one a 10 88 1 12 b 15 09 3 09 c 9 56 2 44 d 9 80 1 57 e 7 82 4 18

The infamous psychologist Dr Visegrips claims that his secret sleep tapes cause people to become better at basic algebra All you have to do the doctor explains is listen to my tapes while you sleep at night and you ll be better at algebra in two months A math teacher at a local high school has expressed interest but demands evidence Five students from this school are randomly selected They take an algebra skills test listen to Dr Visegrips tape for two months while they sleep and then take a second test The test scores are given here Test scores Student A B C D E Pretest 68 69 74 71 65 Posttest70 68 75 72 68 Which of the following is the correct 99 confidence interval for the true ISC

of drivers states that A 95 confidence interval for the mean time it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1 2 to 1 8 seconds Which of the following claims is justified Select one a A reporter claims that any randomly selected driver will take at least 1 2 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him b A reporter claims that the mean amount of time it takes to apply the brakes after seeing the brake lights on a vehicle in front of him is at least 1 2 seconds O c A reporter claims that it takes at least 1 5 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him d A reporter claims that it takes at least 2 seconds to apply the brakes after seeing the brake lights on a vehicle in front of him e A reporter claims that it takes 1 2 or 1 8 seconds to apply the brakes after seeing the brake lights on a vehicle in

speed at which people complete routine tasks Fifteen volunteers are asked to sort 100 red and white beads into two piles according to color once while listening to Handel s Water Music and once in silence the order music or silence first is determined for each subject by the flip of a coin Here are the data along with summary statistics in the last two columns Subject Handel Silence 16 Difference 2 Select one a We want to estimate the mean difference Silence Handel in time to sort the beads with and without music Which of the following is the appropriate 95 confidence interval b 1 C d e 2 3 4 15 17 21 18 17 20 15 3 0 1 2 0 4 2 145 0 4 1 96 41 96 1 96 19 0 18 6 2 145 0 4 2 145 1 96 15 5 67 13 18 21 17 22 1 1 1 96 14 1 96 5 04 5 13 15 15 8 9 10 24 15 25 27 14 3 1 3 11 12 22 30 22 20 32 2 13 14 15 13 15 16 15 13 17 2 1 18 6 19 0 0 4 5

Let S 1 2 3 4 5 6 7 8 9 10 be the universal set Let sets A B and C be subsets of S where Set A 1 3 9 10 Set B 1 4 5 7 10 Set C 1 2 8 LIST the elements in the set An BNC AnBnC LIST the elements in the set AUBUC AUBUC

A test is performed to determine whether The mean verbal SAT score of all the stat students at a university is 580 You perform a test of hypothesis and get a p value of 0 011 Which can we conclude based on this p value Mark all that apply O At the 5 level of significance we would reject the null hypothesis and conclude that the alternative hypothesis is true We would say that the results are statistically significant At the 1 level of significance we would reject the null hypothesis This p value tells us that if the mean SAT score of all stat students at this university were 580 the results from our sample would be surprising At the 5 level of significance the data is sufficient to conclude that the mean verbal SAT score of all stat students at this university is different than 580

6 6 2010 Healthcare Law On June 28 2012 the U S Supreme Court upheld the much debated 2010 healthcare law declaring it constitutional A Gallup poll released the day after this decision indicates that 46 of 1 012 Americans agree with this decision At a 95 confidence level this sample has a 3 margin of error Based on this information determine if the following statements are true or false and explain your reasoning a We are 95 confident that between 43 and 49 of Americans in this sample support the decision of the U S Supreme Court on the 2010 healthcare law O true false b We are 95 confident that between 43 and 49 of Americans support the decision of the U S Supreme Court on the 2010 healthcare law false O true c If we considered many random samples of 1 012 Americans and we calculated the sample proportions of those who support the decision of the U S Supreme Court 95 of those sample proportions will be between 43 and 49 O false Otrue d The margin of error at a 90 confidence level would be higher than 3 O false true

The box and whisker plot below represents some data set What percentage of the data values are between 20 and 76 20 40 60 80 100

For this assignment imagine that you would like to compare the efficacy of two drugs fohkusbehter and kahnsentrayte to treat Attention Deficit Disorder ADD The study will be similar to the one you conducted in the last module with a placebo condition and a dependent variable based on quiz scores

Q If I toss a coin three times what is the modeled probability of throwing exactly two heads A To use the formula above we need to know n S and n E So S HHH HHT HTH HTT THH THT TTH TTT so n S 8 E Set of outcomes with two heads HHT HTH THH so n E 3 n E P E n S 8 2 Toss a coin three times Q The probability of rolling alternating heads and tails is Check Clear Hint P E Q The probability of rolling at least one tail is So P E 3 Q If I roll a pair of fair dice what is the probability of rolling a double both dice show the same number A Here we use the distinguishable dice model whose outcomes are equally likely seen above P E n S 36 E 1 1 2 2 3 3 4 4 5 5 6 6 n E n S 36 61 Check Clear Hint 6 4 Randomly choose a person from a class of 30 in which 10 have scarlet hair 5 have green hair 5 have blue hair and 10 have orange Q If E is the event that a randomly selected person in the class has orange hair then Line Clear

You are dealt a hand of five cards from a standard deck of playing cards The number of possible hands is 2 598 960 The number of possible hands consisting entirely of red cards diamonds and earts is 65 780 and equal to the number of possible hands consisting entirely of any other pair of suits The number of possible hands consisting entirely of diamonds is 1287 and equal to the umber of hands consisting entirely of any other suit The number of possible hands that include no diamonds at all is 575 757 and equal to the number of hands that exclude any other particular suit QThe probability of being dealt a hand that includes at least one diamond is approximately B G L 2215 75 0253 Help C 0005 7785 H M 9747 B 5148 G 5 Help C H Q The probability of being dealt a hand of 5 cards of a single color is approximately 75 D I 0009904 2 023 203 2 597 673 E 5 J D 131 560 2754 25 E 0506 J 001981 F 9995 K 2 533 180 F 25 ore dealt a hand of five cards of the same color from a standard deck of playing cards the probability of having a hand consisting entirely of diamonds is approximately

0 0 t t 2 t t 0 0 t Keypad Keyboard Shortcuts Tables

Fill in the missing probabilities given that the outcome 6 is three times as likely as the outcome 1 The probability that the outcome is at least 3 is he probability that an odd number will come un is Outcome Probability 1 2 3 Check 0 11 0 11 0 11 Clear 4 Check Clear Help Hint 5 0 11

on of estion 5 Use this picture for questions 2 5 Characteristics of Job Applicants d Yes Has High School Diploma No Answer Find P has diploma Round your answer to ONE decimal place Answer Has Experience Yes No 54 27 4 Find P has diploma and experience Round your answer to THREE decimal places 5 Answer Find P has experience has diploma Round your answer to THREE decimal places Answer Find P has no diploma has experience Round your answer to THREE decimal places

2 A dodecahedron die has 12 faces numbered 1 12 The die is weighted in such a way that 1 6 are each equally likely to land facing up but the remaining numbers are each twice as likely to face up as 1 a What is the probability distribution for the face facing up b What is the probability that the dice lands with a 7 facing up twice in succession Hint Similar to Exercise 23 in Section 7 3 of the textbook Solution

with wild mushroom stuffing and gravy is normally distributed with mean 486 and standard deviation 24 Part 1 of 2 a What proportion of servings have between 494 and 510 calories Round the answer to four decimal places The proportion of servings that have between 494 and 510 calories is 0 2108 Part 1 2 Part 2 of 2 b Find the 70th percentile of the number of calories Round the answer to two decimal places The 70th percentile of the number of calories is

Question 3 The following value of the lo

6 Based on a recent Gallup survey we define the following probability model for the number X of daily cups of coffee consumed by Americans X 0 Probability 0 36 1 0 26 2 0 19 3 0 09 4 or more What is the probability that an American consumes 4 or more cups of coffee daily fill in the table

X 0 1 2 3 P x 0 15 0 3 0 2 0 35 Find the mean of this probability distribution Round your answer to one decimal p

d is drawn from a deck of 52 playing cards then what is the probabiltiy of getting a jack or a face care 224 PED P 4 4 104 4

Events A and B are mutally exclusive Find the indicated Probability P A 0 28 P B 0 05 P A or B

Imagine that you are taking a multiple choice quiz written in Norwegian and must guess randomly Each question has 5 choices and 1 correct answer Calculate the probability that you answer the first question correctly answer the first 2 questions correctly answer the first 3 questions correctly answer the first 4 questions correctly Note Enter each answer as a fraction or as a decimal rounded to the nearest thousandth

Demographics of social media news consumers In 2017 the users of Facebook for news was distributed according to the following age groups Age 18 29 A 24 8 30 49 40 1 50 64 24 1 65 11 Percentage Please convert all answers to decimal form a What is the probability that a Facebook News user selected at random is between 18 and 49 inclusive b What is the probability that a Facebook News user selected at random is between 30 and 64 inclusive c What is the probability that a selected Facebook News user is under 65

card is drawn from a deck of 52 playing cards then what is the probabiltiy of getting an Red or a Que