Question 1023575
 
Question: (edited)
By the empirical rule, what percentage of the area under the normal curve lies between μ-3σ and μ+3σ? Put your answer as a percentage.Is the z value, positive or negative?
 
Solution:
A. area between μ-3σ and μ+3σ
Use a normal distribution table, calculator or a software to find 
P(Z<=&mu;-3&sigma;)=0.0013499
P(Z<=&mu;+3&sigma;)=0.9986501
and therefore
area = P(Z<=&mu;+3&sigma;)- P(Z<=&mu;-3&sigma;)
=0.9973002
 
B. Answer in percentage
Multiply the answer in (A) by 100% to get answer as a percentage.
 
C. The sign of values of Z 
Z is calculated by
Z=(X-&mu;)/&sigma;.
When X=&mu;, then Z=0.  
Similarly, when X<&mu; Z is negative, while when X>&mu; Z is positive.
&sigma; is always positive, since it is the square-root of the variance.
Look at the given expressions to determine if the Z-values are positive or negative.