Exam 5: The Standard Deviation As a Ruler and the Normal Model

Suppose that a Normal model describes fuel economy (miles per gallon) for automobiles and that a Toyota Corolla has a standardized score (z-score) of +2.2.This means that Corollas…

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?

The distribution of the diameters of a particular variety of grapes is approximately normal with a standard deviation of 0.3 cm.How does the diameter of a grape at the 67th percentile Compare with the mean diameter?

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 ASQ (American Society for Quality) regularly conducts a salary survey of its membership, primarily quality management professionals.Based on the most recently Published mean and standard deviation, a quality control specialist calculated the z-score Associated with his own salary and found it was -2.50.This tells him that his salary is

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.The typical worker needs five minutes to Adjust to his or her surroundings before beginning duties.What percent of new machine set Ups are completed within 25 minutes to allow for this?

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 between 375 and 425 pounds per square inch?

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?

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?

Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after last week's storm had a z-score of 1.8.This means that the acidity of that rain …

Both SAT and ACT are well-known placement tests that most US colleges require from prospective students to be admitted in their programs.Scores in the SAT test are Approximately normally distributed with a mean of 500 and a standard deviation of 100. Scores in the ACT test are approximately normally distributed with a mean of 18 and a Standard deviation of 6.What would be the score in the SAT test to get the same z-score as The admission requirement of an ACT score of 27?

A soft drink dispenser can be adjusted to deliver any fixed number of centiliters.If the machine is operating with a standard deviation in delivery equal to 0.3 centiliter, what should Be the mean setting so that a 12-centilitre cup will overflow less than 1% of the time? Assume a normal distribution for centiliters delivered.

Light bulbs are measured in lumens (light output), watts (energy used), and hours (life).A standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours.At A local science competition, both light bulbs lasted 750 hours.Which light bulb's life span Was better?

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)?

Adult female Dalmatians weigh an average of 50 pounds with a standard deviation of 3.3 pounds.Adult female Boxers weigh an average of 57.5 pounds with a standard deviation of 1.7 pounds.One statistics teacher owns an underweight Dalmatian and an underweight Boxer.The Dalmatian weighs 45 pounds, and the Boxer weighs 52 pounds.Which dog is More underweight?

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?

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?

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.What percent of The batches of water discharged exceed the 80 ppm standard?