Questions: What is the z score of the location marked " A " ? 0 -2 1 Not enough information to determine.

Transcript text: What is the $z$ score of the location marked " A " ? 0 $-2$ 1 Not enough information to determine.

Solution

Solution Steps

Step 1: Understand the Empirical Rule

The Empirical Rule (or 68-95-99.7 Rule) states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.

Step 2: Analyze the graph

The graph shows a standard normal distribution curve. The markings indicate standard deviations from the mean. The center line represents the mean (z-score of 0). The blue lines enclose 68% of the data, corresponding to one standard deviation on either side of the mean. The orange lines enclose 95% of the data, corresponding to two standard deviations from the mean. Finally, the grey lines enclose 99.7% of the data, corresponding to three standard deviations from the mean. Point A is located at the negative one standard deviation mark.

Step 3: Determine the z-score of A

Since point A is located at -1 standard deviation from the mean, its z-score is -1.