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)

Normal Distribution Graph

P(Z ≤ 1.47) = 0.9292

P(Z > a) = 1 - P(Z ≤ a)

Normal Distribution Graph

P(Z > 1.47) = 1 − P(Z ≤ 1.47) = 1 − 0.9292 = 0.0708

P(Z ≤ −a) = 1 − P(Z ≤ a)

Normal Distribution Graph

P(Z ≤ −1.47) = 1 − P(Z ≤ 1.47) = 1 − 0.9292 = 0.0708

P(Z > −a) = P(Z ≤ a)

Normal Distribution Graph

p(Z > −1.47) = p(Z ≤ 1.47) = 0.9292

P(a < Z ≤ b ) = P(Z ≤ b) P(Z ≤ a)

Normal Distribution Graph

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 )

Normal Distribution Graph

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)]

Normal Distribution Graph

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