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Mixed Probability Questions

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Solve the following problems showing your work:

1. In a poll, respondents were asked whether they had ever been in a car accident. 157 respondents indicated that they had been in a car accident and 117 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?

2. In a certain class of students, there are 12 boys from Wilmette, 3 girls from Kenilworth, 9 girls from Wilmette, 6 boys from Glencoe, 2 boys from Kenilworth and 6 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

3. Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 5 possible answers.

4. Of 1936 people who came into a blood bank to give blood, 200 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

https://brainmass.com/math/probability/mixed-probability-questions-393403

Solution Preview

1. P(accident)
= CountAccident / CountTotal
= 157 / (157 + 117) = 157 / 274 = 0.573 = 0.573 * 100% = 57.3%

2. P(Kenilworth)
= CountKenilworth / CountTotal
= (3 girls + 2 boys) / ...

Solution Summary

The solution provides answers to four probability questions and shows the steps of the calculations.

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Statistics: 23 problem exam

1. Distinguish between descriptive statistics and inferential statistics.

2. Distinguish between and independent and a dependent variable - give example.

3. The annual incomes of the five vice presidents of Erlen industries are
75000 78000 72000 83000 90000

a. What is the range?
b. What is the arithmetic mean income?
c. What is the population variance? The standard deviation?

4. The ages of a sample of Canadian tourists flying to Hong Kong were
32 21 60 47 54 17 72 55 33 41

What is the standard deviation of the sample?

5. A report by the Department of Justice on rape-victims reports on interviews with 3721 victims. The attacks were classified by the age of the victim and the relationship of the victim to the rapists. The results of the study are given in the table below.
Relationship of Rapist
Age of Victim Family Acquaintance or Friend Stranger
under 12 153 167 13
12 to 17 230 746 172
over 17 269 1232 739

a. What is the probability that a victim was under 12 years of age?
b. What is the probability that a victim was between 12 and 17 and that the rapist was a member of the family?
c. What is the probability that a victim was under 12 or that the rapist was an acquaintance or a friend?
d. What is the probability the victim was not under 12 years of age?
e. What is the probability the rapist was not a family member, acquaintance, or friend?

6. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.

a. What is the area between 415 pounds and the mean of 400 pounds?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at random and discovering it has a value of less than 395 pounds?

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a. What percent of the students scored below 320?
b. Twenty percent of the students had a test score above what score?
c. Ten percent of the students had a test score below what score?

8. Ms. Maria Wilson is considering running for mayor of the town of Bono, Ohio. Before completing the petitions, she decides to conduct a survey of voters in Bono. A sample of 400 voters revealed that 300 would support her in the November election.

a. What proportion of the voters in Bono do you estimate would support Ms. Wilson?
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9. Past surveys revealed that 30 percent of the tourists going to Atlantic City to gamble during a weekend spent more than \$1,000. Management wants to update that percentage.

a. Using the .90 degree of confidence, management wants to estimate the percentage of the tourists spending more than \$1,000 within 1 percent. What sample size should be employed?
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10. A new industrial oven has just been installed at the Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour. The first reading taken at 8:00 AM was 340 F. (Only the last two digits are given in the following table).
Time 1 2 3 4
8:00 AM 40 50 55 39
8:30 AM 44 42 38 38
9:00 AM 41 45 47 43
9:30 AM 39 39 41 41
10:00 AM 37 42 46 41
10:30 AM 39 40 39 40

Based upon this initial experience, determine the control limits for the mean temperature.
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11. Seiko purchases watch stems in lots of 10,000. Seiko's sampling plan calls for checking 20 items, and if 3 or fewer are defective, the lot is accepted. Based upon their sampling plan, what is the probability that a lot of 10 percent defective will be accepted?

12. The Board of Realtors of a small city reports that 80% of the houses that are sold have been on the market for more than 6 months. The Board takes a random sample of 15 homes that have recently been sold and counts the numbers that were on the market for more than 6 months. What is the Probability that of 15 homes in the sample:

a. less than 12 have been on the market for more than 6 months?
b. between 8 and 13 have been on the market for more than 6 months?
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d. at most 4 have been on the market for more than 6 months?

13. Hugger Polls contends that an agent conducts 53 in-depth home surveys every week. A streamlined survey form has been introduced and Hugger wants to evaluate its effectiveness. The number of in-depth surveys conducted during a week by a random sample of agents is:
53 57 50 55 58 54 60
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14. The scores of two groups of inmates at Southard Prison on a rehabilitation test are:
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15. Samples of efficiency ratings of employees at Allied Chemicals in plant number 1 and plant number 2 are:
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160 163
160 162
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159 163
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160 162
159
160

At the .02 level test is there a difference in the mean(s) of the employees.

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Small 2 3 3 8
Medium 3 5 6 7
Large 6 7 8 8
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17. Sabin Motorcycle Works plans to develop a brochure for its new revolutionary X2B cycle. One of the facets to be explored and reported on is the speed-mileage question: Is there a linear relationship between the cycle's speed and miles per gallon? Tests on their track revealed the following:
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X Y
40 54
30 60
70 37
50 46
60 48

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Bette Jones 2 4
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Photography 22 337
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40,300 190 14 53 230 1
49,600 121 15 49 370 1
40,800 161 14 44 397 1
40,300 161 14 39 181 1
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40,700 202 14 49 551 0
40,800 184 13 37 370 0
37,100 90 14 43 135 0
39,900 181 14 48 332 1
41,400 143 15 54 217 1
38,000 132 14 44 490 0
39,000 127 14 37 220 0
39,500 153 14 50 270 1
40,600 145 14 50 279 1
41,300 174 15 52 329 1
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42,700 188 15 49 433 1
40,100 153 15 53 333 1
45,600 150 16 58 148 0
40,400 173 13 42 390 1
40,900 163 14 46 142 1
40,100 150 15 50 343 0
39,500 139 14 45 373 0

a. Determine the regression equation.
b. What is the value of R2. Comment on the value.
c. What variables could be drop.
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Year Quarter Sales
1997 1 210
2 180
3 60
4 246
1998 1 214
2 216
3 82
4 230
1999 1 246
2 228
3 91
4 280
2000 1 258
2 250
3 113
4 298
2001 1 279
2 267
3 116
4 304
2002 1 302
2 290
3 114
4 310
2003 1 321
2 291
3 120
4 320

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57 51 30 41 61 34 61 38 29 43
57 28 49 50 20 63 32 42 37 42
49 36 52 57 64 21 22 36 49 42
28 36 24 32 22 57 31 58 22 44
40 28 26 18 60 25 26 52 27 28
48 55 57 27 34 43 42 31 35 56
43 43 32 24 35 27 28 47 32 37
27 41 59 44 26 36 43 33 54 33
62 53 56 19 21 35 32 31 60 29
25 46 25 48 26 42 23 33 54 42

See attached file.

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