Question 1023575: By the empirical rule, what percentage of the area under the normal curve lies between mu - 3sd and mu + 3sd? Put your answer as a percentage.Is the z value, positive or negative?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
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<=μ-3σ)=0.0013499
P(Z<=μ+3σ)=0.9986501
and therefore
area = P(Z<=μ+3σ)- P(Z<=μ-3σ)
=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-μ)/σ.
When X=μ, then Z=0.
Similarly, when X<μ Z is negative, while when X>μ Z is positive.
σ 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.
|
|
|
