Exam 6: Continuous Probability Distributions

The lognormal distribution is clearly negatively skewed for σ > 1.

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 ________.

Examples of random variables that closely follow a normal distribution include the age and the class year designation of a college student.

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 probability density function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable.

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ________.

How many parameters are needed to fully describe any normal distribution?

The average wait time at a McDonald's drive-through window is about three minutes ("The Doctor Will See You Eventually," The Wall Street Journal, October 18, 2010). Suppose the wait time is exponentially distributed. What is the probability that a randomly selected customer will have to wait no more than five minutes?

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require less than 16 minutes to grade?

Which of the following is correct?

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 between $3.70 and $3.90 per gallon?

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.

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?

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 ________.

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?

Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait more than two minutes?

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 9%, with a standard deviation of 12%. The relatively less risky fund promises an expected return and standard deviation of 5% and 8%, respectively. A) Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return? B) Which mutual fund will you pick if your objective is to maximize the probability of earning a return of between 8% and 12%?

The mean travel time to work is 25.2 minutes (U.S. Census). Further, suppose that commute time follows a log-normal distribution with a standard deviation of 10 minutes. What is the probability a randomly selected U.S. worker has a commute time of less than 20 minutes?

The cumulative distribution function is denoted and defined as which of the following?

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 between $325 and $425?