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: What is the expected area of the resulting circular region