Area & Probability
What is the total area under a normal curve?
1
What does a z-score represent?
How many standard deviations a value is from the mean
Area to the right = 1 − what?
Area to the left
Area left = 0.50 → z = ?
0
If μ = 100, σ = 10, x = 110, find z.
1
What is the area to the left of z = 0?
0.5
What is the z-score formula?
z = (x − μ) / σ
How do you find area between two z-scores?
Subtract the smaller area from the larger area
Area left = 0.975 → z ≈ ?
1.96
If μ = 50, σ = 5, x = 40, find z.
-2
If area to the left is 0.84, is the z-score positive or negative?
Positive
If x = μ, what is z?
0
If z₁ = -1 and z₂ = 1, what is the approximate area between?
0.68
Area right = 0.05 → z ≈ ?
1.645
Convert z = 2 to x if μ = 70, σ = 5.
80
If area to the right is 0.10, what is the area to the left?
0.90
If z = -2, where is the value located?
Below the mean
If area left of z₁ is 0.30 and left of z₂ is 0.80, find area between.
0.50
Area between center for 95% → z ≈ ?
±1.96
Formula to convert z to x?
x = μ + zσ
What does area under the curve represent?
Probability
If σ increases, what happens to z (same x)?
Z gets smaller
If area right of z is 0.25, what is left area?
0.75
Area left = 0.025 → z ≈ ?
-1.96
If z = -1.5, μ = 200, σ = 20 → x = ?
170