Answer to Question #204574 in Statistics and Probability for Xharlein

Question

The mean score and standard deviation in the Statistics test are respectively equal to 80 and 2.5, whereas in the Mathematics test the mean score is 70 and the standard deviation is 2. If Liza got a score of 85 in Statistics and a score or 75 in Mathematics in which subject is her standing better assuming normality in both subjects?

Answer 1

$$z=\dfrac{x-\mu}{\sigma}$$

Statistics

$\mu_1=80, \sigma_1=2.5, x_1=85$

$$z_1=\dfrac{x_1-\mu_1}{\sigma_1}=\dfrac{85-80}{2.5}=2$$

Mathematics

$\mu_2=70, \sigma_2=2, x_2=75$

$$z_2=\dfrac{x_2-\mu_2}{\sigma_2}=\dfrac{75-70}{2}=2.5$$

Since $2.5>2,$ then in Mathematics her standing is better.