# Standard normal distribution used to compute probabilities

1. Given that z is a standard normal random variable, compute the following probabilities.

a. P(-1≤z≤0)

b. P(-1.5≤z≤0)

c. P(-2<z<0)

d. P(-2.5≤z≤0)

e. P(-3≤z≤0)

2. Given that z is a standard normal random variable, compute the following probabilities.

a. P(0≤z≤.83)

b. P(-1.57≤z≤0)

c. P(z>44)

d. P(z≥-.23)

e. P(z<1.20)

f. P(z≤-.71)

3. Given that z is a standard normal random variable, compute the following probabilities.

a. P(-1.98≤z≤0)

b. P(.52≤z≤1.22)

c. P(-1.75≤z≤-1.04)

4. Given that z is the standard normal random variable, find z for each situation.

a. The area between 0 and z is .4750b. The area between 0 and z is .2291

c. The area to the right of z is .1314

d. The area to the left of z is.6700

5. 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 between -z and z is .9030

c. The area between -z and z is .2050

d. The area to the left of z is .9948

e. The area to the right of z is.6915

6. Given that z is a standard normal random variable, find z for each situation.

a. The area to the right of z is. 01

b. The area to the right of z is .025

c. The area to the right of z is.05

d. The area to the right of z is .10

https://brainmass.com/statistics/normal-distribution/standard-normal-distribution-used-to-compute-probabilities-125693

#### Solution Summary

The solution computes probabilities given a standard normal random variable.