Question

How do you find the probability of `P(-1.96 < z < 1.96)` using the standard normal distribution?

Answer 1

`P(-1.96 < z < 1.96) = .95 = 95%`

Explanation:

Given: `P(-1.96 < z < 1.96)`, normal distribution

z-tables have z-scores listed and their corresponding probabilities. The probability is the area under the curve from `0` to the probability value. The area under the full curve is

From the z-tables:

`P(Z < 1.96) = .9750`

`P(Z < -1.96) = 0.0250`

To find the probability or area between two values you need to subtract the two values:

`P(-1.96 < z < 1.96) = P(z < 1.96) - P(z < -1.96)`

`= .9750 - .0250 = .95 = 95%`