Question

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?

z = 0, z = 2.14, z = −1.43

Accepted Answer

Step 1: Understand the problem. The histogram represents test scores, and the midpoints A, B, and C are marked. We need to match these midpoints with the given z-scores (z = 0, z = 2.14, z = −1.43) and determine which z-scores are unusual. Recall that z-scores measure how many standard deviations a data point is from the mean. Step 2: Identify the mean and standard deviation. The histogram shows a distribution of scores. The mean is likely near the center of the distribution, which corresponds to the midpoint B (score = 63). The standard deviation can be estimated based on the spread of the data. Step 3: Match z-scores to midpoints. A z-score of 0 corresponds to the mean, so midpoint B (score = 63) matches z = 0. A z-score of −1.43 indicates a value below the mean, so midpoint A (score = 53) matches z = −1.43. A z-score of 2.14 indicates a value above the mean, so midpoint C (score = 78) matches z = 2.14. Step 4: Determine unusual z-scores. A z-score is considered unusual if it is less than −2 or greater than 2. In this case, z = 2.14 is greater than 2, so it is considered unusual. The other z-scores (z = 0 and z = −1.43) are not unusual. Step 5: Summarize the findings. Midpoint B corresponds to z = 0, midpoint A corresponds to z = −1.43, and midpoint C corresponds to z = 2.14. The z-score of 2.14 is considered unusual because it is greater than 2.

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?

z = 0, z = 2.14, z = −1.43

Verified video answer for a similar problem:

Key Concepts

Z-scores

Unusual z-scores

Histograms

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?z = 0, z = 2.14, z = −1.43

Verified video answer for a similar problem:

Key Concepts

Z-scores

Unusual z-scores

Histograms

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?

z = 0, z = 2.14, z = −1.43