Using the Z Table
The Z table gives the probabilities of P (z ≤ k).
The Values of k in the Table
Units and tenths in the column on the left.
Hundredths in the top row.
P(Z ≤ a)
P(Z ≤ 1.47) = 0.9292
P(Z > a) = 1 - P(Z ≤ a)
P(Z > 1.47) = 1 − P(Z ≤ 1.47) = 1 − 0.9292 = 0.0708
P(Z ≤ −a) = 1 − P(Z ≤ a)
P(Z ≤ −1.47) = 1 − P(Z ≤ 1.47) = 1 − 0.9292 = 0.0708
P(Z > −a) = P(Z ≤ a)
p(Z > 1.47) = p(Z ≤ 1.47) = 0.9292
P(a < Z ≤ b ) = P(Z ≤ b) − P(Z ≤ a)
P( 0.45 <Z ≤ 1.47) = P(Z ≤ 1.47) − P(Z ≤ 0.45) =
= 0.9292 − 0.6736 = 0.2556
P(−b < Z ≤ −a ) = P(a < Z ≤ b )
P(−1.47 <Z ≤ − 0.45) = P( 0.45 <Z ≤ 1.47) =
= P(Z ≤ 1.47) − P(Z ≤ 0.45) = 0.9292 − 0.6736 = 0.2556
P(−a < Z ≤ b ) = P(Z ≤ b) − [ 1 − P(Z ≤ a)]
P(-1.47 < Z ≤ 0.45) = P(Z ≤ 0.45) − [ 1 − P(Z ≤ 1.47)]=
= 0.6736 − (1 − 0.9292) = 0.6028
p = K
If the probability value is known, find the value of k that is closest to it in the table.
p = 0.75Z ≤ 0.68
To calculate the variable X, use the standard score formula.
(X − μ)/σ = 0.68X = μ + 0.68 σ
