For the normal distribution with parameters μ = 0, σ = 3; calculate P(x > 1).


To calculate \( P(x > 1) \) for a normal distribution with parameters \( \mu = 0 \) and \( \sigma = 3 \), we first convert the given value of \( x = 1 \) into the standard normal distribution \( Z \), using the z-score formula:

\[
Z = \frac{x - \mu}{\sigma}
\]

Substituting the given values:

\[
Z = \frac{1 - 0}{3} = \frac{1}{3} \approx 0.3333
\]

Next, we find the probability that \( Z \) is greater than 0.3333, which is:

\[
P(Z > 0.3333)
\]

This is calculated as:

\[
P(Z > 0.3333) = 1 - P(Z \leq 0.3333)
\]

Using standard normal distribution tables or a calculator, we find:

\[
P(Z \leq 0.3333) \approx 0.6293
\]

Thus,

\[
P(Z > 0.3333) = 1 - 0.6293 = 0.3707
\]

So, \( P(x > 1) \approx 0.3707 \).

Would you like more details on any step or further questions? Here are 5 related questions you might find interesting:

1. How would you calculate \( P(x < 1) \) for the same distribution?
2. What is the probability that \( x \) lies between -1 and 1 for this distribution?
3. How would you interpret the result of \( P(x > 1) \) in a real-world scenario?
4. What would happen to \( P(x > 1) \) if the standard deviation were increased?
5. How do you calculate \( P(x > 1) \) using a calculator with built-in normal distribution functions?

**Tip:** Remember, in the normal distribution, about 68% of the data lies within one standard deviation from the mean.

For the normal distribution with parameters μ = 0, σ = 3; calculate P(x > 1).

Learn how to calculate P(x > 1) for a normal distribution with mean μ = 0 and standard deviation σ = 3. This problem involves finding the Z-score and using standard normal distribution tables. Suitable for students in Grades 10-12.

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