Use Table A (or the equivalent technology) to find the value z of a standard Normal variable that is closest to having 25% of the observations falling above it.

Question

BlackTom AI · Accepted Answer

The task asks for the z-value on a standard normal distribution such that 25% of observations fall above it. In other words, find z where P(Z > z) = 0.25. This is equivalent to P(Z ≤ z) = 0.75 because the total area is 1.

Using the standard normal table or a calculator, the 0.75 quantile is about z = 0.674..., commonly rounded to 0.67. Therefore, the value that makes the upper tail 25% is around 0.67.

If the problem asks for the closest value, 0.67 is indeed a reasonable approximation.

Note: since there are no answer choices provided in the prompt, we can’t link to a specific option, but the computed z ≈ 0.6745.

Some potential misconceptions: thinking the cutoff corresponds to the lower tail (e.g., z negative) would yield more than 25% above, and selecting z = -0.67 would place 75% above, which is incorrect. Another point: rounding to 0.67 vs 0.68 slightly shifts the tail area; 0.6745 is the precise solution, so 0.67 is the closest commonly used two-decimal value.

Use Table A (or the equivalent technology) to find the value z of a standard Normal variable that is closest to having 25% of the observations falling above it.单项选择题

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