Exam 6: Continuous Probability Distributions

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.

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

Exhibit 6-4.The average time between trades for a high-frequency trading investment firm is 40 seconds.Assume the time between trades is exponentially distributed. Refer to Exhibit 6-4.What is the probability that the time between trades for a randomly selected trade and the one proceeding it is more than a minute?

Exhibit 6-3.Patients scheduled to see their primary care physician at a particular hospital wait,on average,an additional eight minutes after their appointment is scheduled to start.Assume the time that patients wait is exponentially distributed. Refer to Exhibit 6-3.What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?

For any normally distributed random variable with mean μ and standard deviation σ,the percent of the observations that fall between and is closest to ______.

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.

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.

An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90.What is the risk,measured by standard deviation,that this investment manager has assumed in his calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?

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.

The probability P(Z < -1.28)is closest to ____.

The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500.We know that the probability of a randomly selected administrative assistant making a salary between μ - x and μ + x is 0.7416.Find the salary range referred to in this statement.

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

The East Los Angeles Interchange is the busiest freeway interchange in the world.In 2008,an average of 550,000 cars passed through the intersection per day with a standard deviation of 100,000.What is the probability more than 620,000 use the interchange on a random day? Assume the number of cars on the interchange is approximately normally distributed.

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500.Due to budget limitations,it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise.What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

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 average wait time to see a doctor at a maternity ward is 16 minutes.What is the probability that a patient will have to wait between 20 and 30 minutes before seeing a doctor? Suppose the wait time is exponentially distributed.

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4,find the following probabilities. A) b. c. d.

The continuous uniform distribution describes a random variable,defined on the interval [a,b],that has an equally likely chance of assuming values within any subinterval of [a,b] with the same length.

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 exactly 3.7 hours to construct a soapbox derby car.

Sarah's portfolio has an expected annual return at 8%,with an annual standard deviation at 12%.If her investment returns are normally distributed,then in any given year Sarah has approximately ______________________.