Conditional probability worksheet2
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This document presents seven probability problems involving conditional probability and Bayes' theorem. The problems cover topics like the probability of an event given another event, the probability of drawing balls of different colors from an urn, and using Bayes' theorem to calculate the probability someone has a disease based on a test result and prior probability information. Solving several of the problems requires using the law of total probability and Bayes' theorem.
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Learning Objectives:
Chapter 17: Thinking about chance
Explain how random events behave in the short run and in the long run and how random and
haphazard are not the same thing.
Perform basic probability calculations using die rolls and coin tosses.
Define probability, and apply the rules for probability.
Explain whether the law of averages is true.
Explain how personal probability differs from a scientific or experimental probability.
Chapter 18: Probability models
Define a probability model. Create a probability model for a particular storys events.
Apply the basic rules of probability to a story problem.
Calculate probabilities using a probability model, including summing up probabilities or
subtracting probabilities from the total.
Define a sampling distribution.
Chapter 20: The house edge: expected values
Define expected value, and calculate the expected value when given a probability model.
Define the law of large numbers, and explain how it is different from the mythical law of
averages.
Explain how casinos and insurance companies stay in business and make money.
Chapter 13: The Normal distribution
Identify data that is Normally distributed.
Discuss how the shape/position of the Normal curve changes when the standard deviation
increases/decreases or when the mean increases/decreases.
Define the standardized value or Z-score. Calculate the Z-score, and use the Z-score to do
comparisons.
Calculate probabilities and cut-off values using the 68%-95%-99.7% (Empirical) Rule.
Identify the mean, standard deviation, cut-off value, probability, and Z-score on a Normal curve.
Use the Normal table to get percentiles (probabilities) for forward problems and to get Z-scores
in order to determine cut-offs for backward problems using both > and < in the inequalities.
Recognize whether a story is a forward or backward Normal distribution problem, and perform
the appropriate calculations showing correct notation, the initial probability expression, and all
necessary steps.
2
Chapter 21: What is a confidence interval?
Define statistical inference and explain when statistical inference is used.
Explain what the confidence interval means and whether the results refer to the population or
the sample.
Calculate the margin of error and identify the margin of error in a confidence statement.
Explain what type of error is covered in the margin of error.
Determine whether a story is better described with a proportion or a mean.
Use appropriate notation for proportions and means, both in the population and the sample.
Calculate a confidence interval for a proportion and for a mean.
Describe how increasing/decreasing the sample size or confidence level changes the margin of
error (width of the confidence interval).
Apply cautions for using confidence inte ...Exercise 7-1 Q # 10 Number of faculty. the numbers of faculty .docx
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Exercise 7-1
Q # 10
Number of faculty. the numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence. assume .
211
384
396
211
224
337
395
121
356
621
367
408
515
280
289
180
431
176
318
836
203
374
224
121
412
134
539
471
638
425
159
324
Q # 14
Number of jobs. a sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. the population standard deviation is 2.1.
a. find the best point to estimate of the population men.
b.find the 95 % confidence interval of the mean number of jobs.
c.find the 99% confidence interval of the mean number of jobs.
d. which is smaller? explain why.
Q # 18
Day care tuition. a random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. find the 90% confidence interval of the true mean. if a day care center were starting up and wanted to keep tuition low. what would be a reasonable amount to charge?
Exercise 7-2
Q # 8
State Gasoline Taxes. a random sample of state gasoline taxes ( in cents ) is shown here for 12 states. use the data to estimate the true population mean gasoline tax with 90% confidence. does your interval contain the national average of 44.7 cents?
38.4
40.9
67
32.5
51.5
43.4
38
43.4
50.7
35.4
39.3
41.4
Q # 10
Dance Company Students. the number of students who belong to dance company at each of several randomly selected small universities is shown below. estimate the true population mean size of a university dance company with 99% confidence.
21
25
32
22
28
30
29
30
47
26
35
26
35
26
28
28
32
27
40
Exercise 7-3
Q # 6
Belief in haunted places. a random sample of 205 college students were asked if they believed that places could be haunted, and 65 responded yes. estimate the true proportion of college students who believed in the possibility of haunted places with 99% confidence. according to time magazine,37% of americans believe that places can be haunted.
Q # 14
Fighting U.S hunger. in a poll of 1000 likely voters, 560 say that the united states spends too little on fighting hunger at home. find a 95% confidence interval for the true proportion of voters who feel this way.
Exercise 8-2
Q # 4
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Q # 8
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A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, 袖, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.
A.
The z of - 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
B.
The z of - 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
C.
The z of - 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
D.
The z of - 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
Question 2 of 40
2.5 Points
In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, 袖, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes.
A. With a z of -1.2 there is sufficient evidence to conclude that the mean油
value has changed from the 1990 mean of 9.4 minutes.
B. With a P-value of 0.2302 there is not sufficient evidence to conclude油
that the mean value is less than the 1990 mean of 9.4 minutes.
C. With a P-value of 0.2302 there is sufficient evidence to conclude that油
the mean value is less than the 1990 mean of 9.4 minutes.
D. With a z of 1.2 there is not sufficient evidence to conclude that the油
mean value has changed from the 1990 mean of 9.4 minutes.
At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
A.
Ho: 袖 = 18.4 hours H油a油: 袖 孫 18.4 hours
B.
Ho: 袖 = 18.4 hours H油a油: 袖 < 18.4 hours
C.
Ho: 袖 続 18.4 hours H油a油: 袖 < 18.4 hours
D.
Ho: 袖 = 18.4 hours H油a油: 袖 > 18.4 hours
The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test o.6. prob. assignment (1)
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Statistics Homework
1. In her science class, Priscilla read about the growth rate (in centimeters) of two varieties of plants after 20 days. For the data shown below, answer questions a-d.
Variety 1
Variety 2
20 油12 油49 油38 油41 油43 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
18 油54 油62 油59 油53 油25
51 油52 油59 油55 油53 油59 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
13 油57 油42 油54 油56 油38
50 油58 油35 油38 油33 油32 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
41 油36 油50 油62 油45 油55
43 油53
Variety 1
Variety 2
a. 油油油油
Mean: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
a. 油油油油
Mean:
b. 油油油油
Median: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
b. 油油油油
Median:
c. 油油油油
Mode: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
c. 油油油油
Mode:
d. 油C
onstruct a stem and leaf display
with a central stem with Variety 1 on the left and Variety 2 on the right.
Order the leaves with the smallest leaves closest to the stem
.
e. 油油油油
What conclusions can you make from this table?
2. 油油油
Heather recently read about the following distribution which shows the number of pounds of each snack food eaten during the 2012 NCAA Basketball Championship game.
a. 油
Construct a pie chart
for this data 油油油油油油油油
b. 油
Indicate the degree of the central angle
for each snack food
Potato chips 油油油油油油油油油油油油
12.3 million
Tortilla chips 油油油油油油油油油油油
8.4 million
Pretzels 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
7.8 million
Popcorn 油油油油油油油油油油油油油油油油油油
6.3 million
Snack Nuts 油油油油油油油油油油油油油
2.5 million
3. 油油Attached to this exam are two sets of data, CU Womens Softball stats for this season, and a recap of the weather in Portland.
CHOOSE ONE
of these sets of stats, and
a. 油油Make
3
observations of the data.
油油油油油油油油油b. 油油Pose
two
questions about the data that are critical to ask about any set of data.
4. 油油Jorge read that, in the Portland area, each month a household generates an average of 29 pounds of newspaper for recycling. The standard deviation is 2 pounds. Assume the data is normally distributed. What percentage of households 油油油油油油油油油油油油油油油油
a. 油油Recycles between 27 and 31 pounds per month?
b. 油油Recycles less than 33 pounds per month?
5. 油油Andrea obtained a math score of 510 on the SAT; the SAT scores had a mean of 435 and a standard deviation of 105. Her math score on the PSAT was 56; the PSAT scores had a mean of 42 and a standard deviation of 9.5.
a. 油What is her
z-score for the SAT?
b.
What is her
z-score for the PSAT?
c. 油油
Which of the two
test scores from parts
a and b
indicates the
stronger
performance?
Explain.
6. 油油Given the following results on the Stanford Achievement Test where the top row of numbers listed for each subject test shows the raw score for that subtest. The number in the second row of each column shows the
national percentile
.
Verbal
Math
Analytical
Raw Score
350
420
580
Percentile
65
85
92
a.
What
percentage
of the students scored
above
this student.B畛 TEST KI畛M TRA GI畛A K 2 - TI畉NG ANH 10,11,12 - CHU畉N FORM 2025 - GLOBAL SU...
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Exercise 7-1
Q # 10
Number of faculty. the numbers of faculty at 32 randomly selected state-controlled colleges and universities with enrollment under 12,000 students are shown below. use these data to estimate the mean number of faculty at all state-controlled colleges and universities with enrollment under 12,000 with 92% confidence. assume .
211
384
396
211
224
337
395
121
356
621
367
408
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280
289
180
431
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318
836
203
374
224
121
412
134
539
471
638
425
159
324
Q # 14
Number of jobs. a sociologist found that in a sample of 50 retired men, the average number of jobs they had during their lifetimes was 7.2. the population standard deviation is 2.1.
a. find the best point to estimate of the population men.
b.find the 95 % confidence interval of the mean number of jobs.
c.find the 99% confidence interval of the mean number of jobs.
d. which is smaller? explain why.
Q # 18
Day care tuition. a random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. find the 90% confidence interval of the true mean. if a day care center were starting up and wanted to keep tuition low. what would be a reasonable amount to charge?
Exercise 7-2
Q # 8
State Gasoline Taxes. a random sample of state gasoline taxes ( in cents ) is shown here for 12 states. use the data to estimate the true population mean gasoline tax with 90% confidence. does your interval contain the national average of 44.7 cents?
38.4
40.9
67
32.5
51.5
43.4
38
43.4
50.7
35.4
39.3
41.4
Q # 10
Dance Company Students. the number of students who belong to dance company at each of several randomly selected small universities is shown below. estimate the true population mean size of a university dance company with 99% confidence.
21
25
32
22
28
30
29
30
47
26
35
26
35
26
28
28
32
27
40
Exercise 7-3
Q # 6
Belief in haunted places. a random sample of 205 college students were asked if they believed that places could be haunted, and 65 responded yes. estimate the true proportion of college students who believed in the possibility of haunted places with 99% confidence. according to time magazine,37% of americans believe that places can be haunted.
Q # 14
Fighting U.S hunger. in a poll of 1000 likely voters, 560 say that the united states spends too little on fighting hunger at home. find a 95% confidence interval for the true proportion of voters who feel this way.
Exercise 8-2
Q # 4
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Q # 8
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A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, 袖, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.
A.
The z of - 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
B.
The z of - 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
C.
The z of - 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
D.
The z of - 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
Question 2 of 40
2.5 Points
In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, 袖, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes.
A. With a z of -1.2 there is sufficient evidence to conclude that the mean油
value has changed from the 1990 mean of 9.4 minutes.
B. With a P-value of 0.2302 there is not sufficient evidence to conclude油
that the mean value is less than the 1990 mean of 9.4 minutes.
C. With a P-value of 0.2302 there is sufficient evidence to conclude that油
the mean value is less than the 1990 mean of 9.4 minutes.
D. With a z of 1.2 there is not sufficient evidence to conclude that the油
mean value has changed from the 1990 mean of 9.4 minutes.
At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
A.
Ho: 袖 = 18.4 hours H油a油: 袖 孫 18.4 hours
B.
Ho: 袖 = 18.4 hours H油a油: 袖 < 18.4 hours
C.
Ho: 袖 続 18.4 hours H油a油: 袖 < 18.4 hours
D.
Ho: 袖 = 18.4 hours H油a油: 袖 > 18.4 hours
The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test o.6. prob. assignment (1)
6. prob. assignment (1)Karan Kukreja
油
This document contains 20 questions about probability. The questions cover a range of probability concepts, including calculating the probability of individual events, combined probabilities of independent and dependent events, conditional probabilities, and probabilities involving drawing balls from bags with varying compositions.Res 341 final exam
Res 341 final examsmith54655
油
The document provides information about a final exam for RES 341, including multiple choice questions and answers regarding statistics concepts such as confidence intervals, control charts, sampling, and hypothesis testing. It also provides textbook price and sales data to solve problems related to estimating means, variances, and probabilities.Res 341 final exam
Res 341 final examhgfyr767678
油
The document provides information about a final exam for RES 341, including multiple choice questions and answers regarding statistics concepts such as confidence intervals, control charts, sampling, and hypothesis testing. It also provides textbook price and sales data to solve problems related to measures of center, variation, and distributions.Statistics Homework 1. In her science class, Priscilla read abou.docx
Statistics Homework 1. In her science class, Priscilla read abou.docxjensgosney
油
Statistics Homework
1. In her science class, Priscilla read about the growth rate (in centimeters) of two varieties of plants after 20 days. For the data shown below, answer questions a-d.
Variety 1
Variety 2
20 油12 油49 油38 油41 油43 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
18 油54 油62 油59 油53 油25
51 油52 油59 油55 油53 油59 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
13 油57 油42 油54 油56 油38
50 油58 油35 油38 油33 油32 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
41 油36 油50 油62 油45 油55
43 油53
Variety 1
Variety 2
a. 油油油油
Mean: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
a. 油油油油
Mean:
b. 油油油油
Median: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
b. 油油油油
Median:
c. 油油油油
Mode: 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
c. 油油油油
Mode:
d. 油C
onstruct a stem and leaf display
with a central stem with Variety 1 on the left and Variety 2 on the right.
Order the leaves with the smallest leaves closest to the stem
.
e. 油油油油
What conclusions can you make from this table?
2. 油油油
Heather recently read about the following distribution which shows the number of pounds of each snack food eaten during the 2012 NCAA Basketball Championship game.
a. 油
Construct a pie chart
for this data 油油油油油油油油
b. 油
Indicate the degree of the central angle
for each snack food
Potato chips 油油油油油油油油油油油油
12.3 million
Tortilla chips 油油油油油油油油油油油
8.4 million
Pretzels 油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油油
7.8 million
Popcorn 油油油油油油油油油油油油油油油油油油
6.3 million
Snack Nuts 油油油油油油油油油油油油油
2.5 million
3. 油油Attached to this exam are two sets of data, CU Womens Softball stats for this season, and a recap of the weather in Portland.
CHOOSE ONE
of these sets of stats, and
a. 油油Make
3
observations of the data.
油油油油油油油油油b. 油油Pose
two
questions about the data that are critical to ask about any set of data.
4. 油油Jorge read that, in the Portland area, each month a household generates an average of 29 pounds of newspaper for recycling. The standard deviation is 2 pounds. Assume the data is normally distributed. What percentage of households 油油油油油油油油油油油油油油油油
a. 油油Recycles between 27 and 31 pounds per month?
b. 油油Recycles less than 33 pounds per month?
5. 油油Andrea obtained a math score of 510 on the SAT; the SAT scores had a mean of 435 and a standard deviation of 105. Her math score on the PSAT was 56; the PSAT scores had a mean of 42 and a standard deviation of 9.5.
a. 油What is her
z-score for the SAT?
b.
What is her
z-score for the PSAT?
c. 油油
Which of the two
test scores from parts
a and b
indicates the
stronger
performance?
Explain.
6. 油油Given the following results on the Stanford Achievement Test where the top row of numbers listed for each subject test shows the raw score for that subtest. The number in the second row of each column shows the
national percentile
.
Verbal
Math
Analytical
Raw Score
350
420
580
Percentile
65
85
92
a.
What
percentage
of the students scored
above
this student.Recently uploaded (20)
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- 1. Worksheet: Probability Theory by Fachrur Rozi, M.Si CONDITIONAL PROBABILITY AND BAYES THEOREM 1. At Kennedy Middle School,the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology? 2. At a middle school,18% of all students play footballand basketball and 32% of all students play football.What is the probability that a student plays basketball given that the student plays football? 3. In Indonesia, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television? 4. A box contains 5 red balls and 9 green balls. Twoballs are drawn in succession without replacement. That is, the first ball is selected and its coloris noted but it is not replaced, then a second ball is selected. What is the probability that: a. the first ball is green and the second ball is green? b. the first ball is green and the second ball is red? c. the first ball is red and the second ball is green? d. the first ball is red and the second ball is red? 5. The probability that Sam parks in a no-parking zone and gets a parking ticketis 0.06. The probability that Sam has to park in a no-parking zone (he cannot find a legal parking space) is 0.20. Today, Sam arrives at schooland has to park in a no-parking zone. What is the probability that he will get a parking ticket? 6. An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people whovisited his dealership were women. Furthermore, his records show that 37% of the women whovisited his dealership purchased an automobile, while 21% of the men who visited his dealership purchased an automobile. a. What is the probability that a customer entering the showroom willbuy an automobile? b. Suppose a customer visited the showroomand purchased a car. Whatis the probability that the customer was a woman? c. Suppose a customer visited the showroombut did not purchase a car. What is the probability that the customer was a man? 7. Lets return to the scenario that began our discussion: A particular test correctly identifies those with a certain serious disease 94% of the time and correctly diagnoses those without the disease 98% of the time. A friend has just informed you that he has received a positive result and asks for your advice about how to interpret these probabilities. He knows nothing about probability, but he feels that because the test is quite accurate, the probability that he does have the disease is quite high, likely in the 95% range. Before attempting to address your friends concern, you research the illness and discover that 4% of men have this disease. What is the probability your friend actually has the disease? Note: For solve no. 5-7 needs the TheLaw ofTotal Probability andBayes Theorem