6. Normal Distribution and Continuous Random Variables

A continuous random variable X is uniformly distributed with 0 ≤ X ≤ 20.

b. What is P(0 ≤ X ≤ 5)?

A commuter train arrives at a station once every 30 minutes. If a passenger arrives at the station at a random time, what is the probability that the passenger will wait less than 10 minutes?

Determine if each curve (in orange) is a valid probability density function (i.e. if the total area under the function = 1)

What are the two properties that a probability density function must satisfy?

Shade the area corresponding to the probability listed, then find the probability.

Shade the area corresponding to the probability listed, then find the probability.

Problems 11–14 use the information presented in Examples 1 and 2.  

Find the probability that your friend is no more than 5 minutes late.

A continuous random variable X is uniformly distributed with 0 ≤ X ≤ 20.

a. Draw a graph of the uniform density function.

Determine if each curve (in orange) is a valid probability density function (i.e. if the total area under the function = 1)

Problems 11–14 use the information presented in Examples 1 and 2.  

a. Find the probability that your friend is between 15 and 25 minutes late.

Problems 11–14 use the information presented in Examples 1 and 2.  

b. It is 10 A.M. There is a 90% probability your friend will arrive within the next _______ minutes.

A continuous random variable X is uniformly distributed with 0 ≤ X ≤ 20.

c. What is P(10 ≤ X ≤ 18)?