Download Statistics 400 - Lecture 2

Statistics 270 - Lecture 17
• 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
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
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?
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
503.92ml or less
• Over a long period of time that 15.15% of jars have a volume of
more than 502.06ml
• What are the mean and standard deviation of the above normal
distribution for jars of peanut butter
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:
3 / 4 [1  (10  r ) 2 ]; for 9  r  11
f (r )  
0 otherwise

• What is the expected area of the resulting circular region