Question

Cherry trees in a certain orchard have heights that are normally distributed with mean u = 114 inches and standard deviation o = 14 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals.

An agricultural scientist wants to study the tallest 1% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this?

Answer 1

To determine the height that corresponds to the tallest 1% of cherry trees in this orchard, we need to find the 99th percentile of the normal distribution, since the tallest 1% will start from that percentile.

Given:
- Mean (\( \mu \)) = 114 inches
- Standard Deviation (\( \sigma \)) = 14 inches

We'll use the TI-84 Plus calculator to find the height corresponding to the 99th percentile:

1. **Turn on your TI-84 Plus calculator.**
2. **Access the distribution menu**: Press `2nd`, then `VARS` to choose `DISTR`.
3. **Select the inverse normal function**: Choose `invNorm(`, which is usually option `3`.
4. **Input the parameters**:
- Enter `0.99` (representing the 99th percentile).
- Enter the mean (`114`).
- Enter the standard deviation (`14`).

The full command should look like this:

```
invNorm(0.99, 114, 14)
```

5. **Press `ENTER`** to calculate.

The output will give you the height corresponding to the tallest 1% of trees.

After performing the calculation, you would find:

- Height ≈ **144.13 inches** (rounded to two decimal places).

Therefore, the agricultural scientist needs to study all the trees above approximately **144.13 inches**.