Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean $\mu=113$ inches and standard deviation $\sigma=16$ inches. Use the Excel spreadsheet to answer the following. Round the answers to at least four decimal places. Part: $0 / 3$ Part 1 of 3 (a) What proportion of trees are more than 124 inches tall? The proportion of trees that are more than 124 inches tall is

Step 1 ：Given that the heights of the cherry trees in a certain orchard are normally distributed with a mean (\(\mu\)) of 113 inches and a standard deviation (\(\sigma\)) of 16 inches.

Step 2 ：We are asked to find the proportion of trees that are more than 124 inches tall.

Step 3 ：To solve this, we first calculate the z-score for the height of 124 inches. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated as (X - \(\mu\)) / \(\sigma\), where X is the height we are interested in, \(\mu\) is the mean height, and \(\sigma\) is the standard deviation.

Step 4 ：Substituting the given values, we get z = (124 - 113) / 16 = 0.6875.

Step 5 ：After calculating the z-score, we can use a z-table to find the proportion of trees that are more than 124 inches tall. This is equivalent to finding the area under the normal distribution curve to the right of the z-score.

Step 6 ：From the z-table, we find that the proportion of trees that are more than 124 inches tall is approximately 0.2459.

Step 7 ：This means that about 24.59% of the trees in the orchard are more than 124 inches tall.

Step 8 ：Final Answer: The proportion of trees that are more than 124 inches tall is approximately \(\boxed{0.2459}\).