Final answer:
The probability p(z > -2.54) is found by subtracting the area to the left of z=-2.54 from 1, which is 0.3446. For z-scores and related probabilities, a z-table or calculator functions like invNorm can be used.
Step-by-step explanation:
To find the standard normal probability for p(z > -2.54), you need to understand that the probability reflects the area under the standard normal distribution curve to the right of the z-score of -2.54. According to a z-table, the area to the left of a z-score of -2.54 is 0.6554. Knowing that the total area under the curve is 1, you would subtract this value from 1 to find the area to the right, which is 0.3446.
In applications like hypothesis testing, this area to the right corresponds to the p-value when the z-test statistic is negative and the test is one-sided. For two-sided tests, the probability found is often multiplied by two. For example, if you're given a z-test statistic of 0.6, you'd find P(Z > 0.6) and then double it for a two-sided test.
To find specific z-scores such as Z0.01 or Z0.05, you may use a calculator or software with invNorm functions, for instance, invNorm(0.95,0,1) on a TI calculator, which helps to find the z-score when the area to the left is 0.95 (Z0.05).