W Exercise 5 Let x have a density function f(x) =1.5(1-x'), for 0sxsi and f(x) = 0 outside the interval [0, 1]. a) Calculate the mean value of x. b) Calculate the median for the distribution of x. c) Compare your answers to part a) and part b), and comment on the shape of the distribution of x. d) Calculate the standard deviation of x. Exercise 6 A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information: Median = 202.2 lower quartile = 196.0 Upper quartile = 216.8 Three smallest observations 125.8 188.1 193.7 Three largest observations 221.3 230.5 250.2 a) How many mild outliers are in the sample? b) How many extreme outliers are in the sample? Exercise 7 A new car salesperson knows that he sells cars to one customer out of 20 who enter the showroom. The probability that he will sell a car to exactly two of the next three customers is? Exercise 8 A small appliance store has 10 VCR's in stock. Four of the VCR's were damaged in shipment. The owner of the store gives his daughter and his son each a VCR for a birthday present. What is the probability that both the gift VCR's will not be defective