Each student is provided with 15 numbers (corresponding to some selected f values).
1,
3,
,4
12,
21,
33,
38,
43,
56,
67,
87,
98,
100,
110,
123
a) Calculate the mean μf and the standard deviation σf of the given numbers (f).
b) Using the following equation and the calculated mean μfand standard deviation σf,calculate each f(f) value that corresponds to each f.
c) Plot the distribution as an f against f(f) graph.
(Hint: You should be getting a normal distribution curvesimilar to the graph on slide 14 in MAT271E_PART 7.pdf file (M. Bayazıt, B. Oğuz, Fig. 4.1 , pg. 80).
(In this way, you have generated your own normal distribution data f(f), using which, you will do all the following normal distribution calculations.
d) Calculate the mean μ and the standard deviation σ of the f(f) data you generated. Subsequently, calculate the standardized variable z for each f(f) value using the equation on slide 15 (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 17 (M. Bayazıt, B. Oğuz, Table 4.1 , pg. 81).
f) Plot the probabilites obtained from the table against f(f) 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(f)data, using the equations provided on slide 21 (M. Bayazıt, B. Oğuz, pg. 80). Compare those values with themean and the standard deviation values you had already obtained for section d of the homework.
h) Calculate the skewness coefficient of the f(f)data.
