Question

How can the empirical rule be restated in terms of z-scores and percentiles? Restate it for four of the seven z-scores. Hint: Use the definitions of z-score and percentile and avoid use of the phrase standard deviation or the numbers 68, 95, and 99.7. I don't understand this question at all, help please!

a) The empirical rule states that for a given z-score, the corresponding percentile can be found by...
b) The empirical rule does not relate to z-scores and percentiles.
c) The empirical rule states that percentiles are determined by...
d) The empirical rule is not applicable to z-scores.

Answer 1

The empirical rule states that for a given z-score, the corresponding percentile can be found by looking up the area to the left of the z-score in a standard normal distribution table.

Step-by-step explanation:

The empirical rule can be restated in terms of z-scores and percentiles. The empirical rule states that for a given z-score, the corresponding percentile can be found by looking up the area to the left of the z-score in a standard normal distribution table.

For example, if the z-score is -2.5, we can find the corresponding percentile by looking up the area to the left of -2.5 in the table, which is approximately 0.0062 or 0.62%. This means that about 0.62% of the values are below -2.5 standard deviations from the mean.

Similarly, if the z-score is 1.8, we can find the corresponding percentile by looking up the area to the left of 1.8 in the table, which is approximately 0.9641 or 96.41%. This means that about 96.41% of the values are below 1.8 standard deviations from the mean.