1) First, for a sample of size n, we need to divide the area of our PDF into n + 1 region with equal area. In this case, we need n + 1 = 5 regions, each with area 1/5(20%) (See the figure). Use the Normal table, your calculator or JMP to obtain these quantiles. Then obtain the corresponding quantiles from a Normal distribution with mean 25 and standard deviation 5.
2) Plot each z-value along the horizontal axis, and each corresponding x-value along the vertical axis. These points should be collinear. What is the slope and intercept of the line through these points? How do they relate to the distribution of X. You do not need to show your plot, as long as you provide proper calculations.
3) We also looked at the Exponential distribution, and derived the function to compute quantiles to be: the μth quantik is given by xp = βln(1 - p) (when p is between 0 and 1). Find the relevant quantiles for the exponential distributions with β = 1 and β = 25.
4) Again, plot the two sets of points, with the quantiles for β - 1 on the x-axis. What are the slope and intercept of the line that goes through these points?
5) Which distribution better models the impact strength data: the Normal or Exponential distributon?