Question

6) Raul received a score of 74 on a history test for which the class mean was 70 with a standard deviation of 3. He received a score of 70 on a biology test for which the class mean was 70 with standard deviation 7. On which test did he do better relative to the rest of the class?a)biology testb)history test c)the same

Answer 1

The z score value is expressed as

`\begin{gathered} z=(x-\mu)/(\sigma) \\ where \\ x\text{ is the sample score} \\ \mu\text{ is the mean score} \\ \sigma\text{ is the standard deviation of the score} \end{gathered}`

Given that

`\begin{gathered} History: \\ x=74 \\ \mu=70 \\ \sigma=3 \\ Biology: \\ x=70 \\ \mu=70 \\ \sigma=7 \end{gathered}`

To determine which test Raul did better,

step 1: Determine the z score value for the history test.

Thus,

`\begin{gathered} z_(history)=(74-70)/(3)=1.333333333 \\ \end{gathered}`

step 2: Determine the z score value for the biology test.

`z_(biology)=(70-70)/(7)=0`

step 3: Determine the probability that he did better in the history test.

Thus, from the normal distribution table,

`Pr(history)=0.9088`

step 4: Determine the probability that he did better in the biology test.

From the normal distribution table,

`Pr(biology)=0.5`

Since the probability that he did better in history is higher than the probability he did better in the biology test, this implies that he did better in the history test, relative to the rest of the class.

The correct option is B.