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 has a lognormal distribution,what can be said of the distribution of the random variable X?

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

A hedge fund returns on average 26% per year with a standard deviation of 12%.Using the empirical rule,approximate the probability the fund returns over 50% next year.

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?

Suppose Jennifer is waiting for a taxi cab.A taxi cab's arrival time is equally likely at any constant time range in the next 12 minutes. a.Compute the expected arrival time. b.What is the probability that a taxi arrives in three minutes or less?

The annual return of a well-known mutual fund has historically had a mean of about 10% and a standard deviation of 21%.Suppose the return for the following year follows a normal distribution,with the historical mean and standard deviation.What is the probability that you will lose money in the next year by investing in this fund?

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