Question

1) The volume of a shampoo filled into a container is a continuous random variable uniformly distributed with 240 and 260 milliliters. What is the probability that the container is filled with MORE THAN the advertised target of 255 milliliters?

2) The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. What is the probability that you wait between 10 and 20 minutes for a taxi?

Answer 1

1)

X ~ Uniform(a,b) = Uniform (240 , 260)

Where a = 240 , b = 260

P(X > x) = ( b - x) / ( b - a)  

So,  

P( X > 255) = ( 260 - 255) / ( 260 - 240 )

= 0.25

2)

X ~ exp( )

Where mean = 1 / = 10

So = 1 / 10

P( x1 < X < x2) = e^{-x1 *} - e^{-x2 *}

So,

P( 10 < X < 20) = e^-10/10 - e^-20/10

= 0.2325