For a standardized normal distribution, determine a value, say z0, so that P(z z0) = 0.025.

Question

For a standardized normal distribution, determine a value, say z0, so that P(z > z0) = 0.025.

BlackTom AI · Accepted Answer

To tackle a question about the standard normal distribution, we need to relate a right-tail probability to the corresponding z-score on the standard normal curve.
Option 1: 1.24. A z-score of 1.24 leaves a tail probability of about 0.107 in the upper tail (P(Z > 1.24) ≈ 0.107), which is far larger than the requested 0.025. This means 1.24 corresponds to a less extreme value than what we need for a 0.025 upper-tail.
Option 2: 2.14. A z-score of 2.14 gives a smaller upper-tail probability, roughly P(Z > 2.14) ≈ 0.016, which is smaller than 0.025. So while this is closer in the right direction, it represents a tail that is too light to match 0.025 exactly.
Option 3: 1.96. This z-score is the classical 97.5th percentile threshold where about 2.5% of the distribution lies to the right, i.e., P(Z > 1.96) ≈ 0.025. This aligns precisely with the target tail probability given in the problem statement.
Option 4: 1.65. A z-score of 1.65 leaves a right-tail probability of roughly P(Z > 1.65) ≈ 0.049, which is almost double the requested 0.025. This would be too extreme a value for the stated tail probability.
In summary, each option corresponds to a different upper-tail probability, and only one matches the requirement P(Z > z0) = 0.025 exactly (within typical rounding). The comparison shows where the probabilities diverge from 0.025, helping to identify which z0 achieves the target.

OSC 2030-007 Fall 2025 Exam 2

For a standardized normal distribution, determine a value, say z0, so that P(z > z0) = 0.025.

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