Exam 6: Introduction to Continuous Probability Distributions

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes.As a promotion,the company plans to hold a drawing to give away one free vacation to Hawaii for a customer who uses between 400 and 402 minutes during a particular month.Based on the information provided,what proportion of the company's customers would be eligible for the drawing?

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes.The manager has decided to have a signal system attached to the phone so that after a certain period of time,a sound will occur on her employees' phone if she exceeds the time limit.The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls.The time limit should be:

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute.If two students were selected at random,what is the probability that they would both read at less than 400 words per minute?

It has been determined the weight of bricks made by the Dillenger Stone Company is uniformly distributed between 1 and 1.5 pounds.Based on this information,the probability that two randomly selected bricks will each weigh more than 1.3 pounds is 0.16.

In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range,explain which distribution will have the larger standard deviation.

Which of the following probability distributions would most likely be used to describe the time between failures for electronic components?

A continuous random variable approaches normality as the level of skewness increases.

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Based on this information,what is the probability that a specific fare will exceed $15.00?

At the West-Side Drive-Inn,customers arrive at the rate of 10 every 30 minutes.The time between arrivals is exponentially distributed.Based on this information,what is the probability that the time between two customers arriving will exceed 6 minutes?

Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes,then the probability that a customer is served in less than 3 minutes is 0.

The Varden Packaging Company has a contract to fill 50 gallon barrels with gasoline for use by the U.S.Army.The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired.However,the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons.The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline.In order to meet this requirement,Varden should set the mean fill to approximately 49.92 gallons.

The money spent by people at an amusement park,after paying to get in the gate,is thought to be uniformly distributed between $5.00 and $25.00.Based on this,what is the probability that someone will spend between $8.00 and $12.00?

The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456.Based on this information,what are the chances that the revenue on the first show will exceed $800?

For a normal distribution,the probability of a value being between a positive z-value and its population mean is the same as that of a value being between a negative z-value and its population mean.

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work.They can then use the sick leave time any time throughout the year.Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies.The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes.Based on this information,what is the probability that an employee will have less than 20 minutes of unused sick time?

The makers of Sweet-Things candy sell their candy by the box.Based on company policy,the mean target weight of all boxes is 2.0 pounds.To make sure that they are not putting too much in the boxes,the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy.In order to do this,with a mean weight of 2 pounds,what must the standard deviation be? Assume that the box weights are normally distributed.

A study of cars arriving at a parking structure at the local airport shows that the time between arrivals is 1.2 minutes and is exponentially distributed.The probability that more than 2 minutes will elapse between the arrivals of cars is about 0.81.

A major U.S.automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg.A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city.Given this information,what is the city mileage standard deviation for this SUV model?

The time between calls to an emergency 911-call center is exponentially distributed with a mean time between calls of 645 seconds.Based on this information,what is the probability that the time between the next two calls is between 200 and 400 seconds?

The probability distribution for a continuous random variable is represented by a probability density function that defines a curve.