Exam 8: Random Variables and Probability Models

Use the appropriate probability model (Poisson). -For quality control purposes, a company that manufactures copper sheets routinely Takes samples from its production process. Since its product is often used for decorative Purposes, one inspection check involves counting the number of imperfections or flaws On sheets that measure 36 sq. ft. Suppose the average number of imperfections per sheet Of this size is 3. What is the probability that a sheet half this size (18 sq. ft.) has 2 Imperfections?

Solve applications involving expected values. -A local unemployment office keeps track of the number of new claims filed each day. Based on data collected, it determines that the expected number of new claims filed per Day is 2.4 with a standard deviation of 0.8688. Suppose that the office is open five days Per week. The expected number of new claims filed per week at this office is

Use the appropriate probability model (Binomial). -Internet service providers (ISP) need to resolve customer problems as quickly as Possible. For one ISP, past data indicates that the likelihood is .80 that customer calls Regarding Internet service interruptions are resolved within one hour. Out of the next 10 Customer calls about interrupted service, the probability that exactly 7 will be resolved Within one hour is

Use the appropriate probability model (Geometric). -A specific automotive part that a service station stocks in its inventory has an 8% Chance of being defective. Suppose many cars come into the service station needing this Part each week. What is the expected number of parts retrieved until the first defective?

Use the appropriate probability model (Geometric). -A specific automotive part that a service station stocks in its inventory has an 8% Chance of being defective. Suppose many cars come into the service station needing this Part each week. What is the probability that the tenth part retrieved from stock is the First defective?

Suppose that incoming calls per hour to a customer service center of a small credit union are uniformly distributed between 0 and 6 calls. a. What is the probability that fewer than 3 calls are received per hour? b. What is the probability that at least 3 calls are received per hour? c. What is the probability that more than 6 calls are received per hour?

Solve applications involving expected values. -A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year Plus a $25 service charge for each repair needed. The company's research indicates that During a given year 86% of these computers need no repairs, 9% need to be repaired Once, 4% twice, 1% three times, and none required more than three repairs. The standard Deviation of the company's annual expense with the service contract for the computer is

It is estimated that 20% of luxury cars manufactured in 2008 were silver. A car dealership typically sells 20 luxury cars per month. a. What is the probability that 8 of the luxury cars sold per month are silver? b. What is the probability that more than 10 of the luxury cars sold per month are silver? c. How many silver luxury cars would you expect are sold per month?

Find the expected value and standard deviation of a random variable. -A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year Plus a $25 service charge for each repair needed. The company's research indicates that During a given year 86% of these computers need no repairs, 9% need to be repaired Once, 4% twice, 1% three times, and none required more than three repairs. The expected Number of repairs for this kind of computer per year is

Use the appropriate probability model (Poisson). -For quality control purposes, a company that manufactures copper sheets routinely Takes samples from its production process. Since its product is often used for decorative Purposes, one inspection check involves counting the number of imperfections or flaws On sheets that measure 36 sq. ft. Suppose the average number of imperfections per sheet Of this size is 3. What is the probability that a sheet of this size has 2 imperfections?

Use the appropriate probability model (Uniform). -Suppose that incoming calls per hour to a customer service center of a small credit Union are uniformly distributed between 0 and 6 calls. What is the probability that more Than 6 calls are received per hour?

Use the appropriate probability model (Uniform). -Suppose that incoming calls per hour to a customer service center of a small credit Union are uniformly distributed between 0 and 6 calls. The probability that fewer than 3 Calls are received per hour is

Find the expected value and standard deviation of a random variable. -A fast food restaurant just leased a new freezer and food fryer for three years. The Service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 Service charge for each repair needed. The restaurant's research indicates that during a Given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% Twice, 4% three times, and none required more than three repairs. The standard deviation Of the number of repairs for this freezer per year is

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research indicates that during a given year 86% of these computers need no repairs, 9% need to be repaired once, 4% twice, 1% three times, and none required more than three repairs. a. Find the expected number of repairs for this kind of computer per year. b. Find the standard deviation of the number of repairs per year. c. What are the mean and standard deviation of the company's annual expense with the service contract for the computer?

Use the appropriate probability model (Geometric). -A specific automotive part that a service station stocks in its inventory has an 8% Chance of being defective. Suppose many cars come into the service station needing this Part each week. What is the probability that the fourth part retrieved from stock is the First defective?

Use the appropriate probability model (Binomial). -Internet service providers (ISP) need to resolve customer problems as quickly as Possible. For one ISP, past data indicates that the likelihood is .80 that customer calls Regarding Internet service interruptions are resolved within one hour. Out of the next 10 Customer calls about interrupted service, how many would be expected to have their Service problems resolved within one hour?

Find the expected value and standard deviation of a random variable. -A fast food restaurant just leased a new freezer and food fryer for three years. The Service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 Service charge for each repair needed. The restaurant's research indicates that during a Given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% Twice, 4% three times, and none required more than three repairs. The expected number Of repairs for this freezer per year is

Find the expected value and standard deviation of a random variable. -A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year Plus a $25 service charge for each repair needed. The company's research indicates that During a given year 86% of these computers need no repairs, 9% need to be repaired Once, 4% twice, 1% three times, and none required more than three repairs. The standard Deviation in the number of repairs for this kind of computer per year is

Solve applications involving expected values. -A fast food restaurant just leased a new freezer and food fryer for three years. The Service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 Service charge for each repair needed. The restaurant's research indicates that during a Given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% Twice, 4% three times, and none required more than three repairs. The mean restaurant's Annual expense with the service contract for this freezer is

Use the appropriate probability model (Uniform). -Suppose that incoming calls per hour to a customer service center of a small credit Union are uniformly distributed between 0 and 6 calls. The probability that at least 3 calls Are received per hour is