Question

according to the 68-95-99.7 rule, approximately 99.7% of the area in any normal distribution is within 3 standard deviations of the mean \\(\mu\\). the actual number \\(z\\) of standard deviations for 99.7% of all observations within \\(z\sigma\\) of \\(\mu\\) is 2.97. this is different from the 68-95-99.7 rule by \\(\\_\\_\\_\\_\\) standard deviations.

Explanation:

Step1: Identify the two values

The 68 - 95 - 99.7 Rule uses \( z = 3 \) for 99.7% of observations, and the actual value is \( z = 2.97 \).

Step2: Calculate the difference

To find the difference, we subtract the actual value from the value given by the rule. So, the difference is \( 3 - 2.97 \).
\[ 3 - 2.97 = 0.03 \]

Answer:

\( 0.03 \)