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?

For the normal distribution with parameters μ = 4,σ = 3;calculate P(x > 1).

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures.What is the probability that a component will be functioning after 60 hours?

Watersports Rental at Flathead Lake rents jet skis and power boats for day use.Each piece of equipment has a clock that records the time that it was actually in use while rented.The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours.Watersports management has decided to give a rebate to customers who use the equipment for less than 2.0 hours.Based on this information,the probability that a customer will get the rebate is 0.4082.

An assembly process takes between 20 and 40 minutes to complete with the distribution of time thought to be uniformly distributed.Based on this,the percentage of assemblies that require less than 25 minutes is 0.05.

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?

The normal distribution is one of the most frequently used discrete probability distributions.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will 15% of the observations be below?

If the mean,median and mode are all equal for a continuous random variable,then the random variable is normally distributed.

For a standardized normal distribution,calculate P(-1.28 < z < 1.75).

For the normal distribution with parameters μ = 3,σ = 2;calculate P(0 < x < 8).

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.

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.

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?

When a single die is rolled,each of the six sides are equally likely.This is an example of a uniform distribution.

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.Suppose a driver has four consecutive fares that are less than $6.00.What is the probability of this happening?

The standard normal distribution has a mean of 0 and a standard deviation of 1.0.

For a standardized normal distribution,determine a value,say z₀,so that P(-z₀ ≤ z ≤ z₀)= 0.95.

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

The parameters of a normal distribution are the mean and the standard deviation.