Exam 6: Continuous Probability Distributions

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon.What is the probability a randomly chosen gas station charges more than $3.70 per gallon?

If an exponential distribution has the rate parameter λ = 5,what is its expected value?

We are often interested in finding the probability that a continuous random variable assumes a particular value.

When attending a movie,patrons are interested in avoiding the pre-movie trivia games,ads,and previews.It is known that the previews begin at the scheduled movie start time and they last between 5 and 15 minutes.Assume that the time of the previews is uniformly distributed. A)Find the expected time and variance of the movie preview duration. B)What is the probability that on a given day the previews last between 10 and 12 minutes?

The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata.com).In 1980,the inflation rate was above 13%.If the annual inflation rate is normally distributed,what is the probability that inflation will be above 13% next year?

The time of a call to a technical support line is uniformly distributed between 2 and 10 minutes.What are the mean and variance of this distribution?

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours.What is the probability that the battery will last more than 9 hours before running out of power?

Exhibit 6-1.You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough.The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Refer to Exhibit 6-1.Above what temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time?

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 Japan Sumo Association has begun to measure the body fat of wrestlers to try to combat the growing problem of excessive obesity within the sport.As of 2010,the average wrestler weighed 412 pounds.Suppose the weights of sumo wrestlers are normally distributed,with a standard deviation of 37 pounds.What is the probability that a randomly selected wrestler weighs between 350 and 450 pounds?

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

The average annual percentage rate (APR)for credit cards held by U.S.consumers is approximately 15 percent ("Ouch - Credit Card APR Now Tops 15 Percent," Time,January 3,2012).Suppose the APR for new credit card offers is normally distributed with a mean of 15% and a standard deviation of 4%.What APR must a credit card charge to be in the bottom 10% of all cards?

Find the value of z for which the standard normal random variable Z satisfies the following: A) b. c. d.

It is known that the length of a certain product X is normally distributed with μ = 20 inches.How is the probability related to ?

Let the time between two consecutive arrivals at a grocery store check-out line be exponentially distributed with a mean of three minutes.Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

The height of the probability density function f(x)of the uniform distribution defined on the interval [a,b] is ____________.

Jennifer is waiting for a taxi cab.The average wait time for a taxi is six minutes.Suppose the wait time is exponentially distributed.What is the probability that a taxi arrives in three minutes or less?

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?

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.What is the probability a rider must wait more than 1.5 minutes?

Find the probability P(-1.96 ≤ Z ≤ 1.96).