1. Statistics Lecture 17

2. Have covered sections 4.1-4.4
We will NOT be covering 4.5 and 4.6…though they make very enjoyable bedtime reading
Today: Examples from Chapter 4
Will begin Chapter 5 next day

3. Example
Let X be the random variable denoting the time between successive arrivals at the drive-up window at a local McDonald’s
If X has an exponential distribution with l=1
Find the expected times between arrivals
Find the probability that the time between successive arrivals is between 2 and 5 minutes

4. Example (good test question)
Suppose the diameter of a certain variety of tree (full grown) is normally distributed with mean of 8 inches and standard deviation of 3 inches
What is the probability that a randomly selected full grown tree will have a diameter between 9 and 10 inches?
If two trees are randomly selected, what is the probability that at least one has a diameter exceeding 9 inches?

5. Example
The amount of peanut butter in a jar follows a N(m, s2) distribution
Over a long period of time that 97.5% of jars have a volume of ml or less
Over a long period of time that 15.15% of jars have a volume of more than ml
What are the mean and standard deviation of the above normal distribution for jars of peanut butter

6. Example
An ecologist wishes to mark off a circular sampling region having a radius of 10m
The radius of the resulting region is actually a random variable with pdf:
What is the expected area of the resulting circular region