Theoretical calculation

Empirical calculation

z_p

p = Φ (z_p)

φ (z_p)

q_X (p)

$z_{q_X}\left(p\right)=q_Z\left(p\right)$

$s{e}_{q_Z\left(p\right)}$

$z_{q_Z\left(p\right)}$

$z_{q_Z\left(p\right)}^2$

−2

0.0228

0.0540

−1.64

−2.2603

0.6175

−0.4215

0.1777

$-1.\widehat{3}$

0.0912

0.1640

−1.3167

−1.7899

0.3925

−1.1633

1.3532

$-0.\widehat{6}$

0.2525

0.3194

−0.33

−0.3543

0.3041

1.0272

1.0552

0

0.5000

0.3989

0.01

0.1404

0.2802

0.5010

0.2510

$0.\widehat{6}$

0.7475

0.3194

0.3361

0.6148

0.3041

−0.1704

0.0290

$1.\widehat{3}$

0.9088

0.1640

0.8045

1.2964

0.3925

−0.0941

0.0089

2

0.9772

0.0540

1.03

1.6245

0.6175

−0.6081

0.3698

∑

3.2448