Given X = 220, μ = 250, and σ = 50
Calculate P(X < Z)
Z-score formula
Using the Normal Distribution, Calculate P(X < 220)
| Z = | X - μ |
| σ/√1 |
| Z = | 220 - 250 |
| 50/√1 |
| Z = | -30 |
| 50/1 |
| Z = | -30 |
| 50 |
Z = -0.6
From the table below, we see that our Z value is = 0.225747
Z-table Lookup Value
The z-table probability runs from 0 to z and -z to 0
Z value = 0.225747
Since that represents ½ of the graph, we subtract our value from 0.5 → 0.5 - 0.225747
P(x<-0.6) = 0.274253
Final Answer
P(x<-0.6) = 0.274253
