Question

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

Answer 1

1. Statistics

Mean$(μ) =80$

standard Deviation $(σ) =2.5$

$Z=\dfrac{X-μ}{σ}$

$Z=\dfrac{85-80}{2.5}$

$Z=2.0$

2. Math

Mean $(μ) =70$

standard Deviation $(σ) =2.0$

$Z=\dfrac{X-μ}{σ}$

$Z=\dfrac{75-70}{2.0}$

$Z=2.0$

From the standard normal distribution tables

$Z(2.0) = 0.97725$

$Z(2.5) = 0.99379$

Beth has a better score in Math which is better than 99.379$\%$ of the class compared to statistics' 97.725$\%$