Question
Let X be a standard normal random variable. Find P(X > 2.82). Express your answer as a decimal.
Answers
GPT-4o mini
To find \( P(X > 2.82) \) for a standard normal random variable \( X \), we need to look up the value in the standard normal distribution table or use a calculator or software that provides cumulative probabilities for the standard normal distribution.
The standard normal distribution table gives us \( P(X \leq z) \). Therefore, to find \( P(X > 2.82) \), we use the relationship:
\[
P(X > 2.82) = 1 - P(X \leq 2.82)
\]
Using a standard normal distribution table or calculator, we find \( P(X \leq 2.82) \). The value is approximately:
\[
P(X \leq 2.82) \approx 0.9974
\]
Now we can calculate \( P(X > 2.82) \):
\[
P(X > 2.82) = 1 - P(X \leq 2.82) = 1 - 0.9974 = 0.0026
\]
Thus, the probability that \( X \) is greater than 2.82 is:
\[
\boxed{0.0026}
\]
The standard normal distribution table gives us \( P(X \leq z) \). Therefore, to find \( P(X > 2.82) \), we use the relationship:
\[
P(X > 2.82) = 1 - P(X \leq 2.82)
\]
Using a standard normal distribution table or calculator, we find \( P(X \leq 2.82) \). The value is approximately:
\[
P(X \leq 2.82) \approx 0.9974
\]
Now we can calculate \( P(X > 2.82) \):
\[
P(X > 2.82) = 1 - P(X \leq 2.82) = 1 - 0.9974 = 0.0026
\]
Thus, the probability that \( X \) is greater than 2.82 is:
\[
\boxed{0.0026}
\]