Hi

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left 

and %50 to the right



Population: mean = 23, SD = 1

P(x < 21),  z = -2

   P(z < -2) = normalcdf( -10, -2) = .0228  TI syntax is normalcdf(smaller z, larger z) -10 a placeholder

P( 21 ≤ x ≤ 23) = .5-.0228 = .4772  0r 47.72%  

Note: P(x ≤ 23) = .5  

(50% of the Area under the Standard Normal curve is to the left of the mean)

 

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