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

1 Answer
marfre
Mar 30, 2018

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

Explanation:

Given: P(-1.96 < z < 1.96)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 00 to the probability value. The area under the full curve is

From the z-tables:

P(Z < 1.96) = .9750P(Z<1.96)=.9750

P(Z < -1.96) = 0.0250P(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)P(−1.96<z<1.96)=P(z<1.96)−P(z<−1.96)

= .9750 - .0250 = .95 = 95%=.9750−.0250=.95=95%

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