Exam 6: Continuous Probability Distributions

Suppose the round trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50.What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?

Suppose the round trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50.What is the probability that a randomly selected airfare between Boston and San Francisco will be more than $450?

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?

Scores on a business statistics final exam are normally distributed with a mean of 74 and standard deviation of 8.z value for the exam score of 84 equals _____.

The stock price of a particular asset has a mean and standard deviation of $58.50 and $8.25,respectively.Use the normal distribution to compute the 95^th percentile of this stock price.

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. If the miners excavated 1000 tons of dirt,how little gold must they have found such that they find that amount or less only 15% of the time?

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known.

Find the z value such that =0.9082.

A continuous random variable is characterized by uncountable values and can take on any value within an interval.

After a heavy snow,the city of Boston spends millions of dollars plowing the streets.Suppose the amount of time the city must spend before the streets are clear follows a log-normal distribution.Further suppose that the average amount of time is 12 hours and the standard deviation is 5 hours.What percentage of the time does it take more than 10 hours for the streets to be cleared?

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?

The standard normal table is also referred to as the z table.

The mean household income of France is approximately 20,000 euros.Suppose the household income in France has a standard deviation of 10,000 euros and follows a log-normal distribution.Estimate the proportion of French households that have an income of more than 25,000 euros.

A continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)__________.

Given that the probability distribution is normal,it is completely described by its mean μ > 0 and its standard deviation σ > 0.

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

The time you must wait for an Orange Line train of the Massachusetts Bay Transit Authority follows a uniform distribution with a lower bound of 0 minutes and an upper bound of 8 minutes.Jonathan is running to catch the train in order to get to a meeting.He knows that the train needs to arrive within five minutes or else he will be late.What is the probability that he will be late to his meeting?

The probability P(Z < -1.28)is closest 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 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?