Question

graphical analysis #37 - 38. the midpoints a, b, and c are marked on the histogram. match them with the indicated z - scores. which z - scores, if any, would be considered unusual? 37. z = 0, z = 2.14, z = - 1.43, statistics test scores. 38. z = 0.77, z = 1.54, z = - 1.54, biology test scores. comparing test scores for the statistics test scores in exercise 37, the mean is 63 and the standard deviation. for the biology test scores in exercise 38, the mean is 23 and the standard deviation is 3.9. in exercise

Explanation:

Step1: Recall z - score properties

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. A z - score close to 0 represents a data - point close to the mean. Unusual z - scores are generally considered to be $|z|> 2$.

Step2: Analyze Exercise 37

For the statistics test scores with mean $\mu = 63$:

• A z - score of $z = 0$ corresponds to a data - point equal to the mean. Looking at the histogram, the mid - point corresponding to the mean is B.
• For $z = 2.14$, it is a positive z - score, so it corresponds to a value above the mean. The mid - point C is above the mean, so $z = 2.14$ corresponds to C.
• For $z=-1.43$, it is a negative z - score, so it corresponds to a value below the mean. The mid - point A is below the mean, so $z=-1.43$ corresponds to A. And $|z = 2.14|>2$, so $z = 2.14$ is unusual.

Step3: Analyze Exercise 38

For the biology test scores with mean $\mu = 23$:

• For $z = 0.77$, it is a positive z - score, so it corresponds to a value above the mean. The mid - point B is above the mean, so $z = 0.77$ corresponds to B.
• For $z = 1.54$, it is a positive z - score, so it corresponds to a value above the mean. The mid - point C is above the mean, so $z = 1.54$ corresponds to C.
• For $z=-1.54$, it is a negative z - score, so it corresponds to a value below the mean. The mid - point A is below the mean, so $z=-1.54$ corresponds to A. Since $|z| = 1.54<2$, none of these z - scores are unusual.

Answer:

Exercise 37: $z = 0$ corresponds to B, $z = 2.14$ corresponds to C (unusual), $z=-1.43$ corresponds to A.
Exercise 38: $z = 0.77$ corresponds to B, $z = 1.54$ corresponds to C, $z=-1.54$ corresponds to A (none are unusual).