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# Probabilities Standard Normal Variables

1. Given that z is a standard normal variable, compute the following probabilities
a. p(z less than or equal to -1.0)
b. p(z is greater than or equal to 1)
c. p( z is greater than or equal to - 1.5)
d. p(-2.5 less than or equal to z)
e. p(-3 < z is less than or equal to 0)
f. p(-1.98 less than or equal to z less than or equal to .49)
g. p(.52 less than or equal to z less than or equal to 1.22)
h. p(-1.75 less than or equal to z less than or equal to -1.04)

2. Given that z is a standard normal random variable, find z for each situation
a. the area to the left of z is 2119
b. the area etween -z and z is .9030
c. the area between -z and z is .2052
d. the area to the left of z is .9948
e. the area to te right of z is .6915

#### Solution Preview

I use the standard normal distribution table to find all answers.
Problem #1
a. P(z <= -1.0) = 0.5 - P(0 < z < 1) = 0.5 - 0.3413 = 0.1587
b. P(z >= 1) = P(z <= -1.0) = 0.1587
c. P(z >= -1.5) = 0.5 + P(0 < z < 1.5) = 0.5 + 0.4332 = 0.9332
d. P(-2.5 <= z) = P(z >= -2.5) ...

#### Solution Summary

The probabilities standard normal variables are examined.

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