TDSM 4.3

a) Amanda's Z-score on verbal reasoning:

[math]z_v = \frac{X_v - \mu_v}{\sigma_v} = \frac{160-151}{7} = 1.2857[/math]

Amanda's Z-score on quantitative reasoning:

[math]z_q = \frac{X_q - \mu_q}{\sigma_q} = \frac{157-153}{7.67} = 0.5215[/math]

b) She did verbal reasoning section better than quantitative reasoning section, relative to other students.

c) By looking at the Standard normal table, we have:

[math] z_v = 1.2857 \Rightarrow \Phi(z_v) = 0.9015 [/math] so Amanda's percentile on verbal reasoning section is 90.15

[math] z_q = 0.5215 \Rightarrow \Phi(z_v) = 0.6985 [/math] so Amanda's percentile on quantitative reasoning section is 69.85