Cherry trees in a certain orchard have heights that are normally distributed with mean  inches and standard deviation  inches. Use the Round the answers to at least four decimal places.
What is the probability that a randomly chosen tree is between 95 and 105 inches tall?

To solve this problem, we need to calculate the probability that a randomly chosen cherry tree has a height between 95 and 105 inches. Assuming the heights of the trees are normally distributed, we will use the standard normal distribution (Z-distribution) to find this probability.

Given:
- The mean height \( \mu \) (in inches) is unknown.
- The standard deviation \( \sigma \) (in inches) is unknown.

### Approach:
1. **Standardize the Heights**: Convert the heights of 95 inches and 105 inches to Z-scores using the formula:

   \[
   Z = \frac{X - \mu}{\sigma}
   \]

   where:
   - \( X \) is the height of the tree (either 95 or 105 inches),
   - \( \mu \) is the mean height of the trees,
   - \( \sigma \) is the standard deviation of the heights.

2. **Calculate the Probability**: Once we have the Z-scores, we can use standard normal distribution tables (or a calculator) to find the probability that the tree’s height falls between the two Z-scores.

Could you provide the values for the mean \( \mu \) and standard deviation \( \sigma \)? With those, we can continue to calculate the exact probability.

Cherry trees in a certain orchard have heights that are normally distributed with mean inches and standard deviation inches. Use the Round the answers to at least four decimal places. What is the probability that a randomly chosen tree is between 95 and 105 inches tall?

Calculate the probability that a randomly selected cherry tree has a height between 95 and 105 inches. This problem involves normal distribution, Z-scores, and uses the formula Z = (X - μ) / σ to find the solution. Suitable for Grades 11-12 students studying probability and statistics.

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