Exam 6: Continuous Random Variables

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 29.75 and 30.5 inches long?

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

The lifetime of a stereo component is exponentially distributed with mean 1,000 days.What is the probability that the lifetime: Exceeds 1,000 days?

The mean of a standard normal distribution is always equal to _______.

A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n):

At an ocean-side nuclear power plant,seawater is used as part of the cooling system.This raises the temperature of the water that is discharged back into the ocean.The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25ºC. What is the probability that the temperature increase will be between 20 and 22ºC?

For a continuous distribution,the exact probability of a particular value is zero.

The normal approximation of the binomial distribution is appropriate when:

If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10 using the normal approximation to the binomial.

_____ theory is a methodology that attempts to determine the number of servers that strikes an optimum balance between the time customers wait for service and the cost of providing service.

If x is a binomial random variable where n = 100 and p = .1,find the probability that x is less than or equal to 10 using the normal approximation to the binomial.

The average time a subscriber spends reading the local newspaper is 49 minutes.Assume the standard deviation is 16 minutes and that the times are normally distributed. For the 10% who spend the most time reading the paper,how much time do they spend?

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?

Given that X is a normal random variable,the probability that a given value of X is below its mean is ________________.

For a binomial probability experiment,with n = 150 and p = .2,it is appropriate to use the normal approximation to the binomial distribution.

The time between breakdowns of an alarm system is exponentially distributed with mean 10 days.What is the probability that there are no breakdowns on a given day?

The MPG (Miles per Gallon)for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8.What is the probability that the MPG for a selected mid-size car would be: More than 33.2?

A paint sprayer coats a metal surface with a layer of paint between 0.43 and 1.23 millimeters thick.The thickness of the coat of paint is approximately uniformly distributed. What is the probability that paint from this sprayer on any given metal surface will be between 0.75 and 1.05 millimeters thick?

A normal distribution with mean zero and a standard deviation one is called the _____ normal distribution.

A continuous probability distribution having a rectangular shape where the probability is evenly distributed over an interval of numbers is a(n)_____ distribution.