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.

Question

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.