Q1. A study was recently done that emphasized the problem we all face with drink
ID: 3181667 • Letter: Q
Question
Q1. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.Did alcohol play a role 1 Vehicle Involved 2 Vehicles Involved 3 Vehicles Involved Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400
Referring to the TABLE, given that multiple vehicles were involved, what proportion of accidents involved alcohol?
a. 120/170 or 70.59%
b. 120/230 or 52.17%
c. 120/325 or 36.92%
d. 120/400 or 30%
Q2. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur at the same time?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q3. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.
Did alcohol play a role 1 Vehicle Involved 2 Vehicles Involved 3 Vehicles Involved Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400
Referring to the TABLE, given that alcohol was not involved, what proportion of the accidents were single vehicle?
a. 50/75 or 66.67%
b. 25/230 or 10.87%
c. 50/170 or 29.41%
d. 25/75 or 33.33%
Q4. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?
a. 0.08
b. 0.15
c. 0.489
d. 0.511
Q5. If two events are collectively exhaustive, what is the probability that one or the other occurs?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q7. If two events are independent (for example, being struck by lightening and being sued for tax evasion), what is the probability that they both occur at the same time?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q8. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?
a. 0.078
b. 0.1175
c. 0.156
d. 0.310
Q9. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
a. 0.0256
b. 0.0625
c. 0.16
d. 1.00
Q10. In a binomial distribution
a. the random variable X is continuous.
b. the probability of success p is stable from trial to trial.
c. the number of trials n must be at least 30.
d. the results of one trial are dependent on the results of the other trials.
Q11. If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is
a. 0.07
b. 1.45
c. 7.00
d. 14.29
Q12. Another name for the mean of a probability distribution is its expected value.
a. true
b. false
Q13. In a Poisson distribution, the mean and standard deviation are equal.
a. true
b. false
Q14. In a Poisson distribution, the mean and variance are equal.
a. true
b. false
Q15. The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.
a. true
b. false
Q16. The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.
a. true
b. false
Q17. Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there. One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease. Scientists have calculated that the average diameter of the diseased trees is 42 centimeters. They also know that approximately 95% of the diameters fall between 32 and 52 centimeters and almost all of the diseased trees has diameters between 27 and 57 centimeters. When modeling the diameters of diseased trees, which distribution should the scientists use?
a. Poisson distribution
b. Binomial distribution
c. Normal distribution
d. Cumulative distribution
Q18. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?
a. 0.1246
b. 0.5546
c. 0.5865
d. 0.6548
Q19. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.
a. 0.0668
b. 0.0785
c. 0.1248
d. 0.0248
Q20. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is :
a. 0.1253
b. 0.1056
c. 0.0124
d. 0.2145
Q21. Any set of normally distributed data can be transformed to its standardized form.
a. true
b. false
Q22. Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.
a. 1.246
b. 0.9104
c. 0.5846
d. 0.1564
Q23. If a data batch is approximately normally distributed, its normal probability plot would be S-shaped.
a. true
b. false
Q24. For some positive value of X, the probability that a standard normal variable Z is between 0 and 2X is 0.1255. The value of X is
a. 0.99
b. 0.40
c. 0.32
d. 0.16
Q25. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?
a. 0.0668
b. 0.0245
c. 0.1280
d. 1.2045 Q1. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.
Did alcohol play a role 1 Vehicle Involved 2 Vehicles Involved 3 Vehicles Involved Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400
Referring to the TABLE, given that multiple vehicles were involved, what proportion of accidents involved alcohol?
a. 120/170 or 70.59%
b. 120/230 or 52.17%
c. 120/325 or 36.92%
d. 120/400 or 30%
Q2. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur at the same time?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q3. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.
Did alcohol play a role 1 Vehicle Involved 2 Vehicles Involved 3 Vehicles Involved Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400
Referring to the TABLE, given that alcohol was not involved, what proportion of the accidents were single vehicle?
a. 50/75 or 66.67%
b. 25/230 or 10.87%
c. 50/170 or 29.41%
d. 25/75 or 33.33%
Q4. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?
a. 0.08
b. 0.15
c. 0.489
d. 0.511
Q5. If two events are collectively exhaustive, what is the probability that one or the other occurs?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q7. If two events are independent (for example, being struck by lightening and being sued for tax evasion), what is the probability that they both occur at the same time?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.
Q8. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?
a. 0.078
b. 0.1175
c. 0.156
d. 0.310
Q9. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
a. 0.0256
b. 0.0625
c. 0.16
d. 1.00
Q10. In a binomial distribution
a. the random variable X is continuous.
b. the probability of success p is stable from trial to trial.
c. the number of trials n must be at least 30.
d. the results of one trial are dependent on the results of the other trials.
Q11. If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is
a. 0.07
b. 1.45
c. 7.00
d. 14.29
Q12. Another name for the mean of a probability distribution is its expected value.
a. true
b. false
Q13. In a Poisson distribution, the mean and standard deviation are equal.
a. true
b. false
Q14. In a Poisson distribution, the mean and variance are equal.
a. true
b. false
Q15. The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.
a. true
b. false
Q16. The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.
a. true
b. false
Q17. Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there. One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease. Scientists have calculated that the average diameter of the diseased trees is 42 centimeters. They also know that approximately 95% of the diameters fall between 32 and 52 centimeters and almost all of the diseased trees has diameters between 27 and 57 centimeters. When modeling the diameters of diseased trees, which distribution should the scientists use?
a. Poisson distribution
b. Binomial distribution
c. Normal distribution
d. Cumulative distribution
Q18. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?
a. 0.1246
b. 0.5546
c. 0.5865
d. 0.6548
Q19. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.
a. 0.0668
b. 0.0785
c. 0.1248
d. 0.0248
Q20. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is :
a. 0.1253
b. 0.1056
c. 0.0124
d. 0.2145
Q21. Any set of normally distributed data can be transformed to its standardized form.
a. true
b. false
Q22. Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.
a. 1.246
b. 0.9104
c. 0.5846
d. 0.1564
Q23. If a data batch is approximately normally distributed, its normal probability plot would be S-shaped.
a. true
b. false
Q24. For some positive value of X, the probability that a standard normal variable Z is between 0 and 2X is 0.1255. The value of X is
a. 0.99
b. 0.40
c. 0.32
d. 0.16
Q25. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?
a. 0.0668
b. 0.0245
c. 0.1280
d. 1.2045
Explanation / Answer
Answering the first question only because a complete set has been posted.
Probabilty(Alcohol involved/ Multiple vehicles) = (n(Alcohol & 2 vehicles) + n( alcohol & 3 vehicles))/ ((n(2 vehicles) + n( 3 vehicles)) = (100+20)/(275+50) = 120/325=36.92% = b
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