To find the value of \( c \) for which \( P(Z > c) = 0.005 \) from a standard normal distribution, you would typically use a standard normal distribution table or statistical software that provides the z-score corresponding to a given right-tail probability.
The value of \( c \) you're looking for is often referred to as the z-score that corresponds to the 99.5th percentile, because 1 - 0.005 = 0.995, meaning we want the point at which 99.5% of the distribution lies to the left.
You can find this value using statistical tables for the standard normal distribution, which usually give the area to the left of the z-score. Since we want the area to the right, we look for 0.995 in the table.
Alternatively, you can use software or a calculator. In many statistical software packages, you could use an inverse cumulative distribution function (CDF) command. For example, in R, you'd use `qnorm(0.995)` to find the z-score. In Python, with the `scipy.stats` library, you could use `scipy.stats.norm.ppf(0.995)`. These commands will return the z-score where the area to the left of the z-score is 0.995.
Using a standard Z-table or statistical software, the value of \( c \) typically comes out to be approximately \( c = 2.58 \) (rounded to two decimal places).
Therefore, \( P(Z > c) = 0.005 \) for \( c \approx 2.58 \).
For a standard normal distribution, find:
P(z > c) = 0.005
Find c rounded to two decimal places.
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