1. Calculating probabilities for a normal distribution

2. We can compare any normal distribution to the standard normal distribution by using the formula:
X = normal random variable
µ = any value
σ = any value
Z = standard normal
random variable
µ = 0
σ = 1

3. Example
X is a normally distributed random variable with µ =33 and σ = 8. Find:
P(X <20)
X=20
µ =33
Step 1:
Draw a diagram
Step 2:
Use GC

4. Graphics Calculator P(X <20)= 0.0521 Stats Mode Dist = F5 Norm = F1
Ncd = normal distribution probability
P(X <20)=
Upper limit = 20
Lower limit = -∞
µ =33
σ = 8
X=20
µ =33

5. Example
X is a normally distributed random variable with µ =33 and σ = 8. Find:
P(X<20) = P(Z< )
= P(Z < )
=P(Z < )
= 0.5 – =
P(X<20) = P(Z< )
= P(Z < )
=P(Z < )
= 0.5 – =
P(X<20) = P(Z< )
= P(Z < )
=P(Z < )
= 0.5 – =
X=20
µ =33