Where ranges are given as choices pick the correct range For

Where ranges are given as choices, pick the correct range. For example, if you calculate a probability to be .27, you would pick .2-.3. If your answer is .79, your choice would be .7-.8, and so on.

The random variable Z has a standard normal distribution.

a) Find the probability that Z < 0.6?

b) What is the probability that Z < -1.8?

c) What is the probability that Z > -0.7?

d) What is the probability that -1.2 < Z < 0.7 ?

e) What is the probability that |Z| > 1.5?

Solution

a.
P(X < 0.6) = (0.6-0)/1
= 0.6/1= 0.6
= P ( Z <0.6) From Standard Normal Table
= 0.7257                  
RANGE: 7-8
b.
P(X < -1.8) = (-1.8-0)/1
= -1.8/1= -1.8
= P ( Z <-1.8) From Standard Normal Table
= 0.0359                  
RANGE: 0-1

c.
P(X > -0.7) = (-0.7-0)/1
= -0.7/1 = -0.7
= P ( Z >-0.7) From Standard Normal Table
= 0.758                  
RANGE: 7-8
d.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -1.2) = (-1.2-0)/1
= -1.2/1 = -1.2
= P ( Z <-1.2) From Standard Normal Table
= 0.11507
P(X < 0.7) = (0.7-0)/1
= 0.7/1 = 0.7
= P ( Z <0.7) From Standard Normal Table
= 0.75804
P(-1.2 < X < 0.7) = 0.75804-0.11507 = 0.643                  

RANGE: 6-7