Question

So where does the Empirical rule come from? In symmetrical continuous data, a Z-transformed dataset has μ = 0, and σ =1. This is also called a Standard Normal or standardized distribution. What is the probability that a value falls in the interval μ ± 1σ, that is compute the probability P(-1 < Z < 1). Round to four decimals and use leading zeros.

Answer 1

Solution :

Empirical rule :

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

The probability that a value falls in the interval is ,

P(-1 < Z < 1) = P(Z < 1) - P(Z < -1)= 0.8413 - 0.1587 = 0.6826

Probability = 0.6826