How do you find the probability of # 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%#

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%#

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