https://file.aiquickdraw.com/mathbot/file/1727625565821hqdb0jjg.jpg

The problem in the image asks for the value of \( c \) given that the z-scores are normally distributed with a mean of 0 and a standard deviation of 1, and:

\[
P(z > c) = 0.0133
\]

To solve this, we need to find the value of \( c \) where the probability \( P(z > c) = 0.0133 \). This means that the area to the right of \( c \) under the standard normal curve is 0.0133.

1. Look up the value of \( P(z > c) = 0.0133 \) in the standard normal distribution table (or use a calculator or software).
2. Since tables usually provide values for \( P(z < c) \), we'll first find the complement:

\[
P(z < c) = 1 - 0.0133 = 0.9867
\]

3. Now, find the z-score that corresponds to \( P(z < c) = 0.9867 \).

Using the standard normal distribution table or an inverse normal function, we get:
\[
c \approx 2.2132
\]

So, \( c \approx 2.2132 \) (rounded to 5 decimal places).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the value of \( P(z > 2.2132) \) using the z-table?
2. If \( P(z > c) = 0.05 \), what is the value of \( c \)?
3. For a z-score of 1.96, what is the probability that \( P(z < 1.96) \)?
4. How would the calculation change if the mean was not 0 but 1?
5. What is the area under the normal curve between \( z = -1 \) and \( z = 1 \)?

**Tip**: The cumulative probability for a z-score can be quickly found using a scientific calculator or software with an "inverse normal" function, which directly computes the z-value for a given probability.

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > c) = 0.0133, find c (rounded to 5 decimal places).

Solve a normal distribution problem where P(z > c) = 0.0133. Learn how to find the corresponding z-score using the standard normal distribution and inverse normal function. The problem involves key concepts in probability and z-scores, suitable for high school students in Grades 11-12.

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