Answer
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P(x<-0.75) = 0.226627
↓Steps Explained:↓
Given X = 65, μ = 71, and σ = 8
Calculate P(X < Z)
Z-score formula
Using the Normal Distribution, Calculate P(X < 65)
| Z = | X - μ |
| σ/√1 |
| Z = | 65 - 71 |
| 8/√1 |
| Z = | -6 |
| 8/1 |
| Z = | -6 |
| 8 |
Z = -0.75
From the table below, we see that our Z value is = 0.273373
Z-table Lookup Value
The z-table probability runs from 0 to z and -z to 0
Z value = 0.273373
Since that represents ½ of the graph, we subtract our value from 0.5 → 0.5 - 0.273373
P(x<-0.75) = 0.226627
Final Answer
P(x<-0.75) = 0.226627Related Calculators: Negative Binomial Distribution | Geometric Distribution | Binomial Distribution