2.5 Assume that Z represents a normal random variable with mean equals 0 and standard deviation euqals 1.
(1) Determine P (Z>1.50); (2) Determine P (-2.2<Z<2.3); (3) Determine P (0<Z<3).
2.6 The SAT scores for university admission are normally distributed with mean 1055 and standard deviation 75. What fraction of the SAT scores lie between 1100 and 1200?
2.7 Products come form a machine. An inspector picks up four products and measure the diameter of each of the four products. The average of the four measured numbers will be plotted on the control chart shown in the figure. The upper and lower control limits are constructed based on the principle of
limits, i.e., 
below and above
the center line, respectively.
We know that the diameter produced by the machine varies with mean = 100mm and standard deviation = 0.12mm. Calculate the upper control limit and lower control limit for the control chart. Remember that we are using the principle of
limits.
2-8. In problem 7, assume that a new inspector is assigned to this position. Instead of picking up 4 prodcuts, he picks up 9 products. Should the center line be modified? should the control limits be modified? If yes, determine them. Provide your comments when you do your calculations.