Exam 7: The Normal and Other Continuous Distributions

Suppose that the time for e-mail confirmation of an online purchase is uniformly distributed between 1 and 6 minutes. What is the average time for an e-mail Confirmation?

Suppose that the time for e-mail confirmation of an online purchase is uniformly distributed between 1 and 6 minutes. A. What is the probability that an e-mail confirmation arrives within 3 minutes? b. What is the probability that an e-mail confirmation arrives in within 4 minutes? c. What is the average time for an e-mail confirmation?

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?

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. The Standard deviation of the Normal model used to approximate this distribution is

On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by The Poisson distribution. What is the average time between customer arrivals?

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?

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes. A. What is the probability that a problem is diagnosed and fixed within 30 minutes? b. What is the probability that it takes longer than 90 minutes to diagnose and fix a computer problem? c. What is the average time for customer representatives to diagnose and fix computer problems?

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?

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?

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. A. What cutoff value would separate the 2.5% of orders that take the most time to process? b. What cutoff value would separate the 16% of orders that take the least time to process? c. What cutoff values would separate the 95% of orders that are in the middle of the distribution with respect to processing time?

On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by The Poisson distribution. What is the probability that the vendor will have to wait at least 3 minutes for a customer?