The equation for a general normal curve with mean and standa

The equation for a general normal curve with mean and standard deviation is y = e(x )2/(22) 2 . Calculate values for x = 120, 130, \\ldots, 170, 180 where = 150 and = 30. Note that setting = 0 and = 1 in this equation gives the equation for the standard normal curve. (Round your answers to four decimal places.)

x = 120

x = 130

x = 140

x = 150

x = 160

x = 170

x = 180

Solution

So, we apply the formula (X-Mu)/Sigma to normalize each of the Xs.

Mean = 150

Stdev = 30

Hence,

X=120, Z = (120-150)/30 = -1.0000

X=130, Z = (130-150)/30 = -0.6667

X = 140, Z = (140-150)/30 = -0.3333

X = 150, Z = (150-150)/30 = 0.0000

X = 160, Z = (160-150)/30 = .3344

X = 170, Z = (170-150)/30 = .6667

X = 180, Z = (180-150)/30 = 1.0000