QMB 3200 First exam latest update with complete solution

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First exam qmb Question 1 Scenario: There are 800 undergraduates in the College of Science. 300 of these students are enrolled for Physics and 240 are enrolled for Statistics. 300 students are ta ... king neither Physics nor Statistics. Probability that a randomly selected student in the College of Science is enrolled in Physics and Statistics (using 4 decimal places) is: Question 2 Correct Scenario: There are 800 undergraduates in the College of Science. 300 of these students are enrolled for Physics and 240 are enrolled for Statistics. 300 students are taking neither Physics nor Statistics. Enrollment drops and now the following is true: “There are 400 undergraduates in the College of Science. 150 of these students are enrolled for Physics and 120 are enrolled for Statistics. 150 students are taking neither Physics nor Statistics.” Probability that a randomly selected student in the College of Science is enrolled in Physics and Statistics is: Question 3 Scenario: There are 800 undergraduates in the College of Science. 300 of these students are enrolled for Physics and 240 are enrolled for Statistics. 300 students are taking neither Physics nor Statistics. Enrollment stays as the same as before and the following is true: “There are 800 undergraduates in the College of Science. 240 of these students are enrolled for Physics and 300 are enrolled for Statistics. 300 students are taking neither Physics nor Statistics.” Probability that a randomly selected student in the College of Science is enrolled in Physics and Statistics is: Question 4 Scenario: Academic records in the business school of an Ivy League college indicate that for every 100 students taking a quantitative methods course, 30 students drop out in the first week. At the beginning of the current semester, 10 students sign up for the course. Answer the question assuming that this follows a Bernoulli Process (i.e. Binomial Distribution). You can use Binomial Distribution tables from your textbook if you choose. Probability that not more than 2 of the 10 students drop out in the first week: Question 5 Scenario: Academic records in the business school of an Ivy League college indicate that for every 100 students taking a quantitative methods course, 30 students drop out in the first week. At the beginning of the current semester, 10 students sign up for the course. Answer the question assuming that this follows a Bernoulli Process (i.e. Binomial Distribution). You can use Binomial Distribution tables from your textbook if you choose. Probability that none of the 10 students drop out in the first week: (Use Binomial Probability tables) Question 6 Scenario: Academic records in the business school of an Ivy League college indicate that for every 100 students taking a quantitative methods course, 30 students drop out in the first week. At the beginning of the current semester, 10 students sign up for the course. Answer the question assuming that this follows a Bernoulli Process (i.e. Binomial Distribution). You can use Binomial Distribution tables from your textbook if you choose. Probability that exactly 1 of the 10 students drops out in the first week: (Use Binomial Probability tables) Question 7 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. Probability that account selected has balance between $5500 & $6500: Question 8 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. Probability that the account selected has a balance NOT LESS than $7000: Question 9 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. Probability that account selected has a balance which is NOT in the range $6500 to $7000: Question 10 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. If the selected account has a balance in the range $0 to $X with probability of 0.7, the value of X is: Question 11 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. The bank has 2000 defaulted home equity loans. The CFO is considering writing off all loans with balances under $4500. The number of loans that can be written off is: Question 12 Scenario: The “balance” on home equity loans at a bank is a continuous random variable following normal distribution characteristics. The mean value of the normal distribution is $5000. The standard deviation from the mean is $1000. The bank’s Chief Financial Officer (CFO) randomly selects a borrower’s account. Use the Standard Normal Distribution” tables to answer the question. Of the 2000 defaulted loans, if the bank wants to actively pursue borrowers owing more than $8,000, how many such borrowers are there?: Question 13 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Probability the teller takes between 1 & 4 minutes to service a customer: Question 14 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Probability the teller takes exactly 2 minutes to service a customer: Question 15 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Probability that no customers arrive for a half hour rounded to 2 decimals: Question 16 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Probability that no customers arrive for a full hour: Question 17 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Of 100 customers who get serviced by the teller, how many can expect to be serviced in 6 minutes or less?: Question 18 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. Of 200 customers who get serviced by the teller, how many can expect to be serviced in more than 6 minutes?: Question 19 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. The probability that it is Friday and that a student is absent is 3%. Since there are 5 school days in a week, the probability that the school day is Friday is 20%. What is the probability that a student is absent given that today is Friday? Question 20 Scenario: There is only one teller working at a bank. The teller takes an average of 3 minutes to service a customer. Assume that the time the teller takes to service a customer can be represented as an Exponential Probability distribution. Customers arrive at the teller line at the average rate of 1every 10 minutes. Their arrival pattern follows a Poisson distribution. A single six faced die is rolled. The faces are numbered 1 through 6. What is the probability of obtaining a number that is greater than 5, given that the number is even? Question 21 Topic: Sampling. (Ch. 7) Scenario: The following are recorded values of snowfall (in inches) during the entire year at sixteen ski resorts: 64 62 41 50 49 47 33 72 52 40 76 50 26 36 36 57 The mean value of rainfall (in inches) for this population of 16 cities is: Question 22 Topic: Sampling. (Ch. 7) Scenario: The following are recorded values of snowfall (in inches) during the entire year at sixteen ski resorts: 64 62 41 50 49 47 33 72 52 40 76 50 26 36 36 57 The sample mean using the first four values in the first row as your sample is: Question 23 Topic: Sampling. (Ch. 7) Scenario: The following are recorded values of snowfall (in inches) during the entire year at sixteen ski resorts: 64 62 41 50 49 47 33 72 52 40 76 50 26 36 36 57 The sampling error using the first four values in the first row as your sample is: Question 24 Topic: Sampling. (Ch. 7) Scenario: The following are recorded values of snowfall (in inches) during the entire year at sixteen ski resorts: 64 62 41 50 49 47 33 72 52 40 76 50 26 36 36 57 The sampling error using all of the eight values in the first row as your sample is: Question 25 Topic: Sampling. (Ch. 7) Scenario: The following are recorded values of snowfall (in inches) during the entire year at sixteen ski resorts: 64 62 41 50 49 47 33 72 52 40 76 50 26 36 36 57 Which of the following is true?: Question 26 Topic: Sampling Distribution of the Mean with a Finite Population. (Ch. 7) Scenario: Data is being gathered from a population of residents of a remote village. The standard deviation and mean age of this population is 23 years and 60 years respectively. The population consists of a total of 250 residents. If a sample of 45 random residents is selected, what is the probability that the mean of such a sample will not be greater than 62 years? (round your answer to 2 decimal places) a [Show More]

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