The problem shown in the image is asking you to find a value of $a$ such that:

$P(Z > a) = 0.24$

where $Z \sim N(0, 1)$, meaning $Z$ is a standard normal variable (mean $\mu = 0$, standard deviation $\sigma = 1$).

Steps to Solve:

1. You need to find the value of $a$ where the area to the right of $a$ under the standard normal curve is 0.24. This is equivalent to the probability that $Z$, a standard normal variable, is greater than $a$.

2. The total area under the standard normal curve is 1. Since the area to the right of $a$ is 0.24, the area to the left of $a$ is $1 - 0.24 = 0.76$. This area corresponds to the cumulative distribution function (CDF) of the standard normal distribution.

3. Now, you need to find the z-score corresponding to a cumulative probability of 0.76. This can be done using a z-table or a standard normal distribution calculator.

I'll calculate the value of $a$ based on the cumulative probability $P(Z \leq a) = 0.76$.

Let me compute this for you.The value of $a$ such that $P(Z > a) = 0.24$ is approximately $0.71$.

Would you like more details or explanations?

Here are 5 related questions for practice:

1. What is the value of $a$ if $P(Z > a) = 0.05$?
2. How do you calculate the z-score when given a cumulative probability?
3. What is the probability that $Z$ is less than $a = 1.25$ under a standard normal distribution?
4. How does the area under the standard normal curve relate to probabilities?
5. How would this change if $Z$ were a normal variable with mean 3 and standard deviation 2?

Tip: Using a z-table or statistical software can save time when working with normal distributions!