Find the indicated probability using the standard normal distribution.
​P(negative 1.87less thanzless than0​)

To find the indicated probability \( P(-1.87 < z < 0) \) using the standard normal distribution, we can follow these steps:

1. Find the cumulative probability for \( z = -1.87 \).
2. Find the cumulative probability for \( z = 0 \).
3. Subtract the cumulative probability at \( z = -1.87 \) from the cumulative probability at \( z = 0 \).

The cumulative probability for \( z = 0 \) is 0.5 (since it is the mean of the standard normal distribution).

Now, we look up the cumulative probability for \( z = -1.87 \). Using the standard normal distribution table or a calculator:

- The cumulative probability for \( z = -1.87 \) is approximately 0.0307.

Now, we subtract the cumulative probabilities:
\[ P(-1.87 < z < 0) = P(z < 0) - P(z < -1.87) \]
\[ P(-1.87 < z < 0) = 0.5 - 0.0307 = 0.4693 \]

Thus, the probability \( P(-1.87 < z < 0) \) is approximately 0.4693.

Would you like more details on this calculation or have any questions?

Here are 5 related questions you might find helpful:
1. How do you find the cumulative probability for a given z-score?
2. What is the standard normal distribution?
3. How do you use a z-table to find probabilities?
4. Can you explain how to interpret the z-scores in the context of a standard normal distribution?
5. How do you find probabilities for z-scores that are not listed in the z-table?

**Tip:** When working with standard normal distribution tables, always ensure you are referencing the correct side of the distribution (left or right) based on the context of the problem.

Learn how to find the probability P(-1.87 < z < 0 using the standard normal distribution. Step-by-step solution provided with cumulative probabilities and key concepts explained. Suitable for advanced high school students and anyone studying statistics.

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