Find the percent of the total area under the standard normal curve between the following​ z-scores.
zequals=negative 1.3−1.3 and zequals=negative 0.75−0.75

To find the percent of the total area under the standard normal curve between the z-scores \( z = -1.3 \) and \( z = -0.75 \), we can use the standard normal distribution table or a calculator that provides cumulative probabilities for the standard normal distribution.

1. First, find the cumulative probability for \( z = -1.3 \).
2. Next, find the cumulative probability for \( z = -0.75 \).
3. Subtract the cumulative probability at \( z = -1.3 \) from the cumulative probability at \( z = -0.75 \).

Using the standard normal distribution table:

1. The cumulative probability for \( z = -1.3 \) is approximately 0.0968.
2. The cumulative probability for \( z = -0.75 \) is approximately 0.2266.

Now, subtract these probabilities:

\[
0.2266 - 0.0968 = 0.1298
\]

Therefore, the percent of the total area under the standard normal curve between \( z = -1.3 \) and \( z = -0.75 \) is \( 0.1298 \times 100 = 12.98\% \).

Would you like any more details or have any other questions?

Here are 5 questions you might want to ask next:
1. How do you find the area under the normal curve for any given z-score range?
2. What is the significance of the standard normal distribution in statistics?
3. Can you explain how to use the standard normal distribution table?
4. How can we find the z-score for a given percentile?
5. What are some real-life applications of the standard normal distribution?

**Tip:** When working with normal distributions, always sketch the curve and shade the area of interest. This helps in visualizing the problem and understanding which cumulative probabilities to use.

Learn how to find the percent of the total area under the standard normal curve between the z-scores -1.3 and -0.75. Utilize the standard normal distribution table and cumulative probabilities. Suitable for advanced high school students and anyone interested in statistics and normal distributions.

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