Question

n a study of facial​ behavior, people in a control group are timed for eye contact in a​ 5-minute period. Their times are normally distributed with a mean of 187.0 seconds and a standard deviation of 57.0 seconds. Use the​ 68-95-99.7 rule to find the indicated quantity. Find the percentage of times within 57.0 seconds of the mean of 187.0 seconds.

Answer 1

Solution:

mean of 187.0 seconds and a standard deviation of 57.0 seconds.

Empirical Rule

1. Approximately 68% of the data lie within one standard deviation of the mean, that is, in the interval with endpoints μ±σ for populations

2. Approximately 95% of the data lie within two standard deviation of the mean, that is, in the interval with endpoints μ±2σ for populations

3. Approximately 99.7% of the data lie within three standard deviation of the mean, that is, in the interval with endpoints μ±3σ for populations

Using Empirical rule,

The percentage of times within 57.0 seconds of the mean of 187.0 seconds

= μ±σ

= 187.0±57.0

The percentage of times within 57.0 seconds of the mean of 187.0 seconds is 68%