35 122 180 200 398 1783 3450 5610 5600 5870 6690 7892 9820 10005 11031 a) Calculate the mean μ and the standard deviation σ of the given numbers ($). b) Using the following equation and the calculated mean and standard deviation σ, calculate each f(4) value that corresponds to each . f(): 1 √2π -(1-4)2/20 c) Plot the distribution as an against flo) graph. (Hint: You should be getting a normal distribution curve similar to the graph on slide 18 in MAT271E_PART 6.pdf file (M. Bayazıt, B. Oğuz, Fig. 4.1, pg. 80). (In this way, you have generated your own normal distribution data f(), using which, you will do all the following normal distribution calculations. Hint: your variable is now f(o) and you need to make all the rest of the calculations using this variable.) d) Calculate the mean μ and the standard deviation of the f(4) data you generated. Subsequently, calculate the standardized variable z for each f(o) value using the equation on slide 14 (M. Bayazıt, B. Oğuz, Eq. 4.2, pg. 80) e) Find the probabilities corresponding to each z value using the probability distribution function (normal distribution) table given on slide 16 (M. Bayazıt, B. Oğuz, Table 4.1, pg. 81). f) Plot the probabilites obtained from the table against f(b) to form a normal probability paper plot. Plot a trendline to more clearly see the linearity. (Hint: You should be getting a nearly straight line that shows a normal distribution, similar to the graph on slide 20 (M. Bayazıt, B. Oğuz, Fig. 4.2, pg. 82). g) From the normal probability paper plot you obtained, again find the mean and the standard deviation of the f(o) data, using the equations provided on slide 21 (M. Bayazıt, B. Oğuz, pg. 80). Compare those values with the mean and the standard deviation values you had already obtained for section d of the homework. h) Calculate the skewness coefficient of the f(4) data.