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.