Question

A student scores $56$ on a geography test and $246$ on a mathematics test. The geography test has a mean of $80$ and a standard deviation of $20$. The mathematics test has a mean of $300$ and a standard deviation of $36$. If the data for both tests are normally distributed, on which test did the student score better?

Answer 1

Step-1: Given data:

In geography:

Student score $=56$

Mean $=80$

Standard deviation $=20$

In mathematics:

Student score $=246$

Mean $=300$

Standard deviation $=36$

Normally distributed.

Step-2: Finding $Z$ test for Geography:

We know that,

$Z=\frac{x-\mu }{\sigma }$ $x$ is given value, $\mu$ mean,$\sigma$ standard deviation

So here,

$$\begin{gathered} Z=\frac{56-80}{20} \\ =\frac{-24}{20} \\ =-1.2 \end{gathered}$$

Step-3: Finding $Z$ test for Mathematics:

We know that,

$Z=\frac{x-\mu }{\sigma }$ $x$ is given value, $\mu$ mean,$\sigma$ standard deviation

So here,

$$\begin{gathered} Z=\frac{246-300}{36} \\ =\frac{-54}{36} \\ =-1.5 \end{gathered}$$

Step-4: Comparing the $Z$ test values:

The $Z$ test value for Geography $=-1.2$

The $Z$ test value for Geography $=-1.5$

$-1.5<-1.2$

Hence, in geography test student score better.