https://file.aiquickdraw.com/mathbot/file/17274738964241lffdqpi.jpg

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!

Let Z ~ N(0,1), Find a so that P(Z > a) = 0.24

This problem involves finding the value of 'a' for a standard normal distribution Z ~ N(0, 1) where P(Z > a) = 0.24. Learn how to solve this using cumulative distribution function (CDF) and understand key concepts in probability and statistics.

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