91Ó°ÊÓ

Find the median of the exponential probability density function. $$ f(t)=\frac{1}{9} e^{-t / 9},[0, \infty) $$

Waiting Time Buses arrive and depart from a college every 30 minutes. The probability density function for the waiting time \(t\) (in minutes) for a person arriving at the bus stop is $$f(t)=\frac{1}{30}, \quad[0,30]$$ Find the probabilities that the person will wait (a) no more than 5 minutes and (b) at least 18 minutes.

Demand The daily demand for gasoline \(x\) (in millions of gallons) in a city is described by the probability density function $$f(x)=0.41-0.08 x, \quad[0,4]$$ Find the probabilities that the daily demand for gasoline will be (a) no more than 3 million gallons and at least 2 million gallons.

Education The scores on a national exam are normally distributed with a mean of 150 and a standard deviation of \(16 .\) You scored 174 on the exam. (a) How far, in standard deviations, did your score exceed the national mean? (b) What percent of those who took the exam had scores lower than yours?

Demand The daily demand \(x\) for a certain product (in thousands of units) is a random variable with the probability density function \(f(x)=\frac{1}{25} x e^{-x / 5},[0, \infty)\) (a) Determine the expected daily demand. (b) Find \(P(x \leq 4)\).