6. Normal Distribution and Continuous Random Variables

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

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

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

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

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?

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.

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.

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

b. What is P(0 ≤ X ≤ 5)?

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

c. What is P(10 ≤ X ≤ 18)?

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