The critical value z.05 is the .95-quantile for a standard normal distribution.

Compute z.05.

Question

The critical value z.05 is the .95-quantile for a standard normal distribution.

Compute z.05.

BlackTom AI · Accepted Answer

The prompt asks for the critical value z.05, defined as the .95-quantile of a standard normal distribution.

First, recognize what the .95-quantile means: it is the value z such that P(Z ≤ z) = 0.95 for Z ~ N(0,1).

Since there are no provided answer options to evaluate, we proceed to determine z by consulting the standard normal distribution or its inverse CDF.

Using a standard normal table or a calculator for the inverse CDF, we seek z satisfying Φ(z) = 0.95.

From the properties of the standard normal distribution and common reference values, Φ(1.645) ≈ 0.95, since 1.645 is a well-known 95th percentile critical value.

Therefore, the value that satisfies the condition P(Z ≤ z) = 0.95 is approximately z = 1.645.

To cross-check, one can also use the symmetry of the normal distribution and interpolation from z-values around 1.64–1.65 to confirm that the 0.95 quantile lies near 1.645.

BTRY3010/BTRY5010/STSCI2200/STSCI5200 Lecture#21 (Pages 102-103)

The critical value z.05 is the .95-quantile for a standard normal distribution. Compute z.05.

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