Exam 6: Continuous Random Variables

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

During the past six months,73.2 percent of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.Find the probability that a household spent more than $16.00 on sugar.

At an oceanside 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 25°C.What is the expected value of the temperature increase?

The thickness of a randomly selected metal piece is a ___________ random variable.

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time is between 2 and 4 minutes?

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.

Consider a normal population with a mean of 10 and a variance of 4.Find P(X > 18).

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20.What percentage of the time will the number of boxes received weekly be less than 160?

A property of continuous distributions is that:

The binomial random variable x consists of n = 60 trials and has the probability of failure q = 0.4.Using the normal approximation,compute the probability of 32 successes.

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 of at least 10 minutes?

If the random variable x is normally distributed,68.26 percent of all possible observed values of x will be within two standard deviations of the mean.

The lifetime of a stereo component is exponentially distributed with mean 1,000 days.What is the probability that the lifetime is greater than or equal to 700 days?

During the past six months,73.2 percent of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.99 percent of the households spent less than what amount?

What is the probability that a standard normal random variable will be between -2 and 2?

While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the standard deviation of the water depth?

Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons.Because of a current problem with the distribution of water to its citizens,the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water.What should he use as the water limit for a person to qualify for a city tax rebate?

_____________ values of the standard deviation result in a normal curve that is narrower and more peaked.

The US local airport keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals.The stem-and-leaf plot of the data for one year is below. 76 9 77 114 78 79 07 80 88 81 2 82 1 83 88 Compute the standardized quartile value O_i for i = 11.

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution.In this industry,a firm with a standard normal variable value of z = 1: