Final answer:
To find the probability that z is beyond the inner fences, calculate the z-scores and use a z-table to find the areas under the normal curve. The same method can be used to find the probability that z is beyond the outer fences.
Step-by-step explanation:
The probability that z is beyond the inner fences can be found by finding the area under the normal curve beyond the inner fences. To find the inner fences, you need to calculate the z-scores. The z-scores can be found using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Once you have the z-scores, you can use a z-table to find the area under the normal curve beyond the z-scores. The probability that z is beyond the inner fences is the sum of the areas beyond the z-scores.
The outer fences can be found by multiplying the inner fences by a constant, usually 1.5 or 3. The probability that z is beyond the outer fences can be found using the same method as finding the probability beyond the inner fences. However, this time you need to find the z-scores for the outer fences.