Exam 6: Continuous Probability Distributions

On a particular busy section of the Garden State parkway in New Jersey,police use radar guns to detect speeding drivers.Assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.What is the probability of a waiting time in excess of 25 minutes between successive speeders?

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour.Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.

For σ < 1,the lognormal distribution somewhat resembles the _______ distribution.

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.What is the probability a rider waits less than two minutes?

You work in marketing for a company that produces work boots.Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use.They find that the boots wear out in an average of 208 days,but the exact amount of time varies,following a normal distribution with a standard deviation of 14 days.For an upcoming ad campaign,you need to know the percent of the pairs that last longer than six months-that is,180 days.Use the empirical rule to approximate this percent.

For any normally distributed random variable with mean μ and standard deviation σ,the proportion of the observations that fall outside the interval [μ - σ,μ + σ] is the closest to _____.

Let the household income of residents of the United States be represented by Y = e^X,where X is normally distributed.In 2006,the mean U.S.household income was approximately $50,000.Suppose the standard deviation was 16,000.Estimate the proportion of U.S.households that have an income less than 80,000.

Gold miners in Alaska have found,on average,12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of 3 ounces.Assume the amount of gold found per 1000 tons of dirt is normally distributed. What is the probability the miners find between 10 and 14 ounces of gold in the next 1000 tons of dirt excavated?

The exponential distribution is based entirely on one parameter called the ______ parameter.

The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.

Which of the following is not a characteristic of a probability density function f(x)?

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80.Find the value x such that P(X ≤ x)= 0.0606.

The letter Z is used to denote a random variable with any normal distribution.

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5.Find the value x such that P(X ≥ x)= 0.1736.

A daily mail is delivered to your house between 1:00 pm and 5:00 pm.Assume delivery times follow the continuous uniform distribution.Determine the percentage of mail deliveries that are made after 4:00 pm.

The average time between trades for a high-frequency trading investment firm is 40 seconds.Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is more than a minute?

Find the z value such that .

If the mean and the standard deviation of the underlying normal random variable equals respectively µ = 2 and σ = 1,the mean of a lognormal random variable equals _____.

A soft drink company fills two-liter bottles on several different lines of production equipment.The fill volumes are normally distributed with a mean of 1.97 liters and a variance of 0.04 (liter)². a.Find the probability that a randomly selected two-liter bottle would contain between 1.95 and 2.03 liters. b.If X is the fill volume of a randomly selected two-liter bottle,find the value of x for which P(X > x)= 0.3228.