Probability Questions and Answers

A veterinarian treated 7 dogs this morning The list below gives the weights in pounds of each dog 24 3 29 24 8 38 62 Find the range of the data set

A sample of 900 computer chips revealed tha promotional literature claimed that more than 0 05 level to support the company s claim

Listed below are the amounts of net worth in millions of dollars of the ten wealthiest celebrities in a country Construct a 95 confidence interval What does the result tell us about the population of all celebrities Do the data appear to be from a normally distributed population as required 153 264 215 179 175 157 What is the confidence interval estimate of the population mean 146 5 million 201 1 million Round to one decimal place as needed 150 150 150 145 What does the result tell us about the population of all celebrities Select the correct choice and if necessary fill in the answer box es to complete your choice OC We are confident that 95 of all celebrities have a net worth between Round to one decimal place as needed OA We are 95 confident that the interval from million to million actually contains the true mean net worth of all celebrities Round to one decimal place as needed 0 O B Because the ten wealthiest celebrities are not a representative sample this doesn t provide any information about the population of all celebrities million and S million

Suppose that a random sample of 18 adults has a mean score of 63 on a standardized personality test with a standard deviation of 6 A higher score indicates a more personable participant If we assume that scores on this test are normally distributed find a 90 confidence interval for the mean score of all takers of this test Give the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to one decimal place If necessary consult a list of formulas Lower limit Upper limit X

24 6 O C Frequency 7 3 2 11 3 14 8 11 11 1 2 12 6 6 Create a histogram with 5 classes Choose the correct histogram below OA Aouenber 064240 4 8 12 16 Data Value 04 8 12 16 Data Value Q Q 43 Q 8 2 10 08 12 15 10 0 OB O D Frequency Jouenberg SMYNAME 420 H 04 8 12 16 Data Value H 4 8 12 16 Data Value G G O Q

A modified box and whisker plot is a box and whisker plot that uses symbols to identify outliers The horizontal line of a modified box and whisker plot extends as far as the minimum data entry that E not an outlier and the maximum data entry that is not an outlier a Identify any outliers and b draw a modified box and whisker plot that represents the data set Use open circles to plot any outliers 56 59 76 2 50 30 44 50 49 53 48 26 94 19 63 60 48 40 a Identify any possible outliers Select the correct choice below and if necessary fill in the answer box to complete your choice OA The outlier s is are Type an integer or decimal Use a comma to separate answers as needed OB There are no outliers

Let X be the number of packages being malled by a randomly selected customer at a certain shipping facility Suppose the 2 3 1 p x 0 1 0 2 0 3 0 4 X PX 4 a Consider a random sample of size n 2 two customers and let X be the sample mean number of packages shipped Obtain the probability distribution of X 2 5 3 1 5 3 5 4 1 b Refer to part a and calculate P X 2 5 2 c Again copsider a random sample of size n 2 but now focus on the statistic R the sample range difference between the largest and smallest values in the sample Obtain the distributic R Hint Calculate the value of R for each outcome and use the probabilities from part a 2 R 1 3 0 P R d If a random sample of size n 4 is selected what is P X 1 5 Hint You should not have to list all possible outcomes only those for which x 1 5

A service station has both self service and full service islands On each island there is a single regular unleaded pump with two hoses Let X denote the number of hoses being used on the self service island at a particular time and let Y denote the number of hoses on the full service island in use at that time The joint pmf of X and Y appears in the accompanying tabulation p x y X 1 a Given that X 1 determine the conditional pmf of Y i e Pyx 011 Py x 1 1 Py x 211 Round your answers to four decimal places 0 1 2 PY X Y 1 y 0 1 2 Py x 12 y 2 1 0 03 0 01 0 06 0 20 0 08 0 0 10 0 06 0 14 0 32 0 06 X X 0 06 b Given that two hoses are in use at the self service island what is the conditional pmf of the number of hoses in use on the full service island Round your answers to four decimal places 0 1 2 0 20 X X 0 14 0 08 X X 0 32 RACTICE ANOTHER x c Use the result of part b to calculate the conditional probability P Y 1 X 2 Round your answer to four decimal places P Y 1 X 2 0 3846 d Given that two hoses are in use at the full service island what is the conditional pmf of the number in use at the self service island Round your answers to four decimal places 1 2 0

You would like to construct a 95 confidence interval to estimate the p random sample of such incomes and compute the mean of the sample a a What is the best point estimate based on the sample to use for dollars b For each of the following sampling scenarios determine which dis for the 95 confidence interval for the population mean In the table Z refers to a standard normal distribution and t refers Sampling scenario

6 Suppose the researchers test the hypotheses Ho P 0 Ha B 0 The P value of the test is A less than 0 01 B between 0 10 and 0 05 C between 0 05 and 0 01 none of the above D

Felipe and his family are relocating to Los Angeles and have found a great area in which to live The mean price among the homes in the area is 760 000 with a standard deviation of 19 750 They purchased a home for 775 000 a Find the z score of the price of Felipe s home relative to the prices among the homes in the area Round your answer to two decimal places Z 0 b Fill in the blanks to interpret the z score of the price of Felipe s home Make sure to express your answer in terms of a positive number of standard deviations Felipe s home price was standard deviations Choose one the mean price among the homes above below X C

A sample of 800 computer chips revealed

A doctor wants to estimate the mean HDL cholesterol of all 20 to 29 year old females How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99 confidence assuming s 14 2 based on earlier studies Suppose the doctor would be content with 95 confidence How does the decrease in confidence affect the sample size required Click the icon to view a partial table of critical values A 99 confidence level requires subjects Round up to the nearest subject

A college food court surveyed students to gather information about the types of drinks 688 students were surveyed in all 304 of the students drink milk 323 of the students drink tea 119 of the students drink both milk and tea 197 of the students drink both milk and coffee 221 of the students drink both tea and coffee 88 of the students drink all three types of drinks milk tea coffee 126 of the students don t drink any of these three types of drinks milk tea cof Construct a Venn diagram illustrating these results Then answer the question All students in the survey Drink milk C C Drink tea How many of the st neither tea nor coffe students

year There are several other fishing boats that participate in this competition Among all of the competitors the number of fish caught this year had a mean of 49 fish and a standard deviation of 9 fish Karen caught 41 fish a Find the z score of the number of fish that Karen caught relative to the numbers of fish caught among all the competitors Round your answer to two decimal places Z 0 b Fill in the blanks to interpret the z score of the number of fish that Karen caught Make sure to express your answer in terms of a positive number of standard deviations The number of fish that Karen caught was standard deviations Choose one the mean number of fish caught among all the competitors X

For the prostate cancer dataset the different age distribution of white men and black men in New York created the illusion that both groups have similar PC death rates This is an example of PC death No PC death Total Rate per 100 0000 PC death No PC death Total Rate per 100 0000 Under 65 years old White Black 76 18 396 899 396 917 4 5 4 177 823 4 177 899 1 8 65 Years of Age White Men 65 Years of Age O causation Simpson s paradox O reverse association lack of association All ages White 1 359 4 736 887 4 738 246 28 7 Black 121 418 871 418 992 28 9 PC death No PC death Total Rate per 100 0000 Age 65 and older White Black 1 282 102 559 075 21 973 560 357 22 075 228 8 462 1 65 Years of Age 65 Years of Age Black Men

When examining a linear relationship between two quantitative variables the correlation coefficient r represents the percent of variation in y that can be explained by the model O is the slope of the regression line measures both the strength and the direction of the relationship O measures the direction of the relationship O is not appropriate measures the strength of the relationship

Association however strong does NOT NECESSARILY imply O causation O correlation O regression conclusion O confounding success good experimentation

A bag contains 19 blue 28 purple 21 red and 29 orange balls You pick one ball at random Find the probability that it is not blue P not blue

Of all the permutations of the letters in the word DOG if you choose one at random what is the probability that it is an actual English word

A newsletter publisher believes that

K 3 A certain species of animal has a probability of any one offsp remaining probabilities on the tree diagram and use that informa offspring that are all females given that the first is a female

On a survey 7 students reported how many minutes it takes them to travel to school Here are their responses 6 13 14 10 8 13 8 Send data to calculator Find the mean travel time for these students If necessary round your answer to the nearest tenth

You wish to test the claim that the population proportion is less than 0 46 at a significance level of a 0 02 Hop 0 46 Hapo v 0 46 0 B I Part 2 of 6 385 in which there are 148 successful observations For this test you You obtain a sample of size n should NOT use the continuity correction and you should use the normal distribution as an approximation for the binomial distribution What is the critical value for this test Report answer accurate to three decimal places OF critical value 2 054 What is the test statistic for this sample Report answer accurate to three decimal places Part 3 of 6

Use the Laplace transform to solve the given initial value problem y 5y e6t y 0 2 y t

A t distribution with 6 degrees of freedom is graphed below The region under the curve to the right of tog is shaded The area of this region is 0 8 0 8 0 8 0 4 X 03 0 2 0 1 Find the value of to 8 Round your answer to three decimal places 0 Area 0 8

The proportion p of residents in a community who recycle has traditionally been 60 A policy maker claims that the proportion is less than 60 now that one of the recycling centers has been relocated If 145 out of a random sample of 250 residents in the community said they recycle is there enough evidence to support the policy maker s claim at the 0 05 level of significance Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places 0 e Is there enough evidence to support the policy maker s claim that the proportion of residents who recycle is less than 60 O Yes No X X O S OSO P Q 00 ORD D

Consider the following data set Round your answers to the nearest hundredth as needed 55 47 73 70 88 65 88 55 64 88 Mean Median Mode Range Sample Standard Deviation

Your manufacturing plant produces air bags and it known that 60 of them are defective Five air bags are tested Compute the probability distribution of the binomial variable described above and use it to compute the probability that if five air bags are tested at least one will be defective and at least one will not Step 1 Recall that a Bernoulli trial is an experiment that has two possible outcomes One outcome is called a success and the other outcome is called a failure If X is the number of successes in a sequence of n independent Bernoulli trials then we can use the following formula where p is the probability of success and q 1 p is the probability of failure P X x C n x p q x Here we can define success to be that a selected air bag is defective We are given that 60 of the air bags are defective so the probability p that a selected air bag is defective is given by p 0 6 0 6 Step 2 The probability of failure is given by q 1 p Since p 0 60 we have q 0 4 n Five air bags will be randomly selected so we have a series of five independent Bernoulli trials Therefore Step 4 The probability P 1 x 4 is given by the following Step 3 We are to find the probability that of the five air bags selected at least one will be defective and at least one will not Therefore we wish to find the probability that there is at least one success but at least one failure In other words the probability that the number of successes is at least one but no more than four So we need to calculate 1 x 4 0 4 P X 1 C P 1 x 4 P X 1 P X 2 P X 3 P X 4 We will use the independent trials formula four times to calculate each of the values P X 1 P X 2 P X 3 and P X 4 We begin by calculating P X 1 which is the probability when x 1 Recall that we previously determined that n 5 p 0 60 and q 0 40 To avoid intermediate rounding errors do not round the result P X x C n x pxq x 5 1 0 60 0 405 1

Based on a survey assume that 38 of consumers are comfortable having drones deliver their purchases Suppose that we want to find the probability that when four consumers are randomly selected exactly two of them are comfortable with delivery by drones Identify the values of n x p and q The value of n is Type an integer or a decimal Do not round

The effectiveness of a blood pressure drug is being investigated An experimenter finds that on average the reduction in systolic blood pressure is 37 3 for a sample of size 26 and standard deviation 17 4 Estimate how much the drug will lower a typical patient s systolic blood pressure using a 80 confidence level Assume the data is from a normally distributed population Enter your answer as a tri linear inequality accurate to three decimal places

You receive a brochure from a large university The brochure indicates that the mean class size for full time faculty is fewer than 32 students You want to test this claim You randomly select 18 classes taught by full time faculty and determine the class size of each The results are shown in the table below At a 0 10 can you support the university s claim Complete parts a through d below Assume the population is normally distributed 32 31 OA Ho 232 Ha 32 29 28 OD Ho H 32 Ha 232 32 34 30 32 a Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and Ha 35 30 OB Ho H 32 Ha 32 O E Ho 32 Ha 32 41 30 24 32 26 30 OC Ho H 32 H 32 OF Ho 32 Ha H 32 28 28

In a random sample of eleven people the mean driving distance to work was 20 3 miles and the standard deviation was 6 2 miles Assume the population is normally distributed and use the t distribution to find the margin of error and construct a 90 confidence interval for the population mean Interpret the results Identify the margin of error Round to one decimal place as needed CITS

IGN News wants to construct a 93 confidence interval for the proportion of households in California who own a gaming console a A previous survey conducted in 2012 estimated the proportion to be 0 35 Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 02 b Estimate the sample size needed if no estimate for p is available c If IGN News wanted to estimate the proportion in the entire United States rather than in just California would the necessary sample size be larger smaller or about the same Larger Smaller The Same

Births are approximately Uniformly distributed between the 52 weeks of the year They can be said to follow a Uniform distribution from 1 to 53 a spread of 52 weeks Round answers to 4 decimal places when possible a The mean of this distribution is b The standard deviation is c The probability that a person will be born at the exact moment that week 15 begins is P x 15 d The probability that a person will be born between weeks 4 and 43 is P 4 x 43 e The probability that a person will be born after week 23 is P x 23 f P x 18 x 28 g Find the 32nd percentile h Find the minimum for the upper quartile

The mean income for people in a certain city in thousands of dollars is 36 with standard deviation 60 thousands of dollars A pollster draws a sample of 40 people to interview What is the probability that the mean income of the sampled people is more than 22 thousands of dollars If there are two answers list both answers separated by a comma

In a program designed to help patients stop smoking claim that 81 of patients stop smoking when given su

Percent of children 30 20 10 O Without character Taste the same c Would it also be correct to present this data in a single pie chart With character O Yes a pie chart would be appropriate because the three taste preferences make up one whole O Yes a pie chart would be appropriate because it is the best way to display categorical data O No a pie chart would not be appropriate because all children eat Graham crackers O No a pie chart would not be appropriate because the three taste preferences do not make up one whole d What do the data suggest about the influence of cartoon characters on Graham cracker preference in young children O The data show that the minority of the children in this study preferred the crackers with a popular cartoon character whereas less than 10 preferred the crackers without the character This suggests that popular cartoon characters do not influence food choices in young children O The data show that the majority of the children in this study preferred the crackers with a popular cartoon character whereas less than 2 preferred the crackers without the character This suggests that popular cartoon characters influence food choices in young children The data show that the majority of the children in this study preferred the crackers with a popular cartoon character whereas less than 10 preferred the crackers without the character This suggests that popular cartoon characters influence food choices in young children O The data show that the number of children in this study who preferred the crackers with a popular cartoon character about the same as the number who preferred the crackers without the character This suggests that popular cartoon

www awu aleks com alekscgi x Practice Test Statis Question 20 of 24 1 12 13 For each variable determi

Suppose that resting pulse rates among healthy adults are normally distributed with a mean of 74 beats per minute and a standard deviation of 20 beats per minute Use this table or the ALEKS calculator to find the percentage of healthy adults who have resting pulse rates that are less than 102 beats per minute For your intermediate computations use four or more decimal places Give your final answer to two decimal places for example 98 23

Fie chart below shows the percentage of total revenue that a publisher receives from various types of publications Use this chart to answer the questions 7 Cookbooks Magazines Textbooks Nonfiction Poetry Paperbacks a Which category accounts for approximately one fourth of the publisher s total revenue Select One b Approximately what percentage of the total revenue comes from Nonfiction and Textbooks combined Write your answer as a multiple of 10 that is 10 20 30 0 c If the revenue from Paperbacks is 15 of the total revenue approximately what percentage of the total revenue comes from Nonfiction O 5 O 10 33 X O 45

The following summarizes the number of fiction books read last summer by a sample of 29 students at a certain college Number of students Number of books 2 books 9 13 5 1 3 4 5 What is the mean number of books read Round your answer to at least one decimal place

www awu aleks com alekscgi x Isl exe 10 u lg OSTATISTICS Histograms for grouped data The following are distances in miles traveled to the 7 2 37 32 27 22 16 31 31 31 25 25 2 Send data to calculator Draw the histogram for these data using an initial cl or remove classes from the figure Label each class Frequency

We want to conduct a hypothesis test of the claim that for middle aged adults the population mean of their cholesterol levels is less than 191 6 mg We choose dL mg a random sample of such levels The sample has a mean of 193 6 and a standard deviation of 19 5 dL mg dL For each of the following sampling scenarios choose an appropriate test statistic for our hypothesis test on the population mean Then calculate that statistic Round your answers to two decimal places a The sample has size 10 and it is from a normally distributed population with an unknown standard deviation 0 0 0 32 OIt is unclear which test statistic to use b The sample has size 19 and it is from a population with a distribution about which we know very little 0 0 ot 0 It is unclear which test statistic to use

A sample of 1400 computer chips reve company s promotional literature clain sufficient evidence at the 0 02 level to State the null and alternative hypothes

Question Part 2 o A questionnaire was given to students was How stressed have you been in th with 0 being not stressed at all and 10 b

Outliers have VERY LITTLE OR NO EFFECT on which of the following Check all that apply Mean Mode Range Standard Deviation Median

Use the following sample to estimate a population mean 7 7 16 9 0 8 27 3 23 6 58 9 3 48 4 22 9 7 7 Assuming the population is normally distributed find the 99 confidence interval about the population mean Enter your answer as an open interval i e parentheses accurate to two decimal places 99 C I

A bag with 12 marbles is given 5 marbles are blue 4 are red and 3 are Green If only a marble will be randomly picked from the bag What is the probability that the marble chosen is Green 1 Point Probability of an EVENT happening The number of ways a particular event outcome can happen Total of ALL possible outcoms

RANDOM VARIABLES AND DISTRIBUTIONS Computing expected value in a game of chance ain Your answer is incorrect a Your answer is incorrect b Your answer is incorrect B