Exam 7: The Normal and Other Continuous Distributions

According to the Census Bureau, 64.5% of Americans owned their own home in 2013. A local real estate office wants to see if this is the case for its area. The office selects a random sample of 200 people to estimate the percentage who own their own homes. A. Verify that the normal model can be used to approximate the binomial in this situation. b. What is the probability that at least 140 people own their own home?

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean Of 22 minutes and a standard deviation of four minutes. What percent of new machine Set ups take more than 30 minutes?

Based on data collected from its production processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a Mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square Inch. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will Have breaking strengths greater than 412.5 pounds per square inch?

The unemployment rate of persons with a disability is typically higher than for those with no disability. Recent statistics report that this rate is 13.4%. An advocacy group in A large city located in the southeastern region of the U.S. selected a random sample of 250 persons with a disability. What is the probability that no more than 30 persons in this Sample are unemployed?

The unemployment rate of persons with a disability is typically higher than for those with no disability. Recent statistics report that this rate is 13.4%. An advocacy group in a large city located in the southeastern region of the U.S. selected a random sample of 250 persons with a disability. A. Verify that the normal model can be used to approximate the binomial in this situation. b. What is the probability that no more than 30 persons in this sample are unemployed?

A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement. The time it takes to process phone orders is normally Distributed with a mean of 6 minutes and a standard deviation of 2.5 minutes. The time it Takes for an arrangement to be completed is normally distributed with a mean of 35 Minutes and a standard deviation of 8.6 minutes. What is the probability that it will take More than 50 minutes to process a phone order and complete the floral arrangement at This flower shop?

Suppose that the time for e-mail confirmation of an online purchase is uniformly distributed between 1 and 6 minutes. The probability that an e-mail confirmation arrives Within 3 minutes is

The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes. What Cutoff values would separate the 16% of orders that take the least time to process?

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes. What is the probability that it Takes longer than 90 minutes to diagnose and fix a computer problem?

Porcelain tile is often recommended over ceramic tile because its breaking strength tends to be higher therefore making it more durable and long lasting. Based on data collected from its production processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch. A. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths between 375 and 425 pounds per square inch? b. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch? c. Based on the 68-95-99.7 Rule, describe the breaking strength of the weakest 2.5% of its popular porcelain tile?

A company's manufacturing process uses 500 gallons of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the Water into a nearby lake. To meet federal regulations the treated water must not contain More than 80 parts per million (ppm.) of the chemical. The machine's output can be Described by a normal model with standard deviation 4.2 ppm. The company's lawyers Insist that not more than 2% of the treated water should be over the limit. To achieve This, to what mean should the company set the scrubbing machine?

The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time A. less than 19.5 hours? b. between 20 and 22 hours?

The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes. What Cutoff value would separate the 2.5% of orders that take the most time to process?

A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement. The time it takes to process phone orders is normally distributed with a mean of 6 minutes and a standard deviation of 2.5 minutes. The time it takes for an arrangement to be completed is normally distributed with a mean of 35 minutes and a standard deviation of 8.6 minutes. A. What are the mean and standard deviation for the total time to process a phone order and complete the floral arrangement at this flower shop? b. What is the probability that it will take more than 50 minutes to process a phone order and complete the floral arrangement at this flower shop?

Suppose that the time for UPS confirmation by e-mail or text of a door delivery is uniformly distributed between 5 and 10 minutes. A. What is the probability that the confirmation arrives within 6 minutes? b. What is the probability that the customer will have to wait no more than 7 minutes for a confirmation? c. What is the probability that the customer will have to wait at least 8 minutes for a confirmation?

A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement. The time it takes to process phone orders is normally Distributed with a mean of 6 minutes and a standard deviation of 2.5 minutes. The time it Takes for an arrangement to be completed is normally distributed with a mean of 35 Minutes and a standard deviation of 8.6 minutes. What is the standard deviation for the Total time to process a phone order and complete the floral arrangement at this flower Shop (assuming times are independent)?

The unemployment rate of persons with a disability is typically higher than for those with no disability. Recent statistics report that this rate is 14.5%. An advocacy group in A large city located in the southeastern region of the U.S. selected a random sample of 250 persons with a disability. What is the probability that at least 20 persons in this Sample are unemployed?

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes. What is the probability that a Problem is diagnosed and fixed within 30 minutes?

A company's manufacturing process uses 500 gallons of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. To meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical. Because a fine is charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water. The machine's output can be described by a normal model with standard deviation 4.2 ppm. A. What percent of the batches of water discharged exceed the 80 ppm standard? b. The company's lawyers insist that not more than 2% of the treated water should be over the limit. To achieve this, to what mean should the company set the scrubbing machine? Assume the standard deviation does not change.

According to the Census Bureau, 64.5% of Americans owned their own home in 2013. A local real estate office wants to see if this is the case for its area. The office selects a Random sample of 200 people to estimate the percentage who own their own homes. What is the probability that at least 140 people own their own home?