In a certain population of clover, the number of flowers on each plant is approximately normally distributed with a mean of 10.8 flowers/plant and a standard deviation of 2.1 flowers/plant. What percentage of the plants fall between 8 and 11 flowers?

Use David's excellent "normal distribution" calculator

http://davidmlane.com/hyperstat/z_table.html

click on "area from a value"
enter the data, click on "between" and enter 8 and 11 to get .4467

You can enter the data directly, no need to find z-scores first.
If you have converted to z-scores, enter 0 for mean and 1 for sd, your input for 8 would be -1.3333
and the input for 11 would be .095238
to get the same result of .4467

To find the percentage of plants that fall between 8 and 11 flowers, we need to calculate the area under the normal distribution curve between these two values.

First, let's standardize the values using the formula for z-score:
z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For the lower bound, x = 8:
z1 = (8 - 10.8) / 2.1

For the upper bound, x = 11:
z2 = (11 - 10.8) / 2.1

Next, we can use a standard normal distribution table or a calculator to find the percentage or area under the curve between these two z-scores. This area represents the proportion of plants that fall between 8 and 11 flowers.

The standard normal distribution table provides the area to the left of each z-score. Since we need the area between z1 and z2, we can find the area to the left of z2 and subtract the area to the left of z1.

Let's assume z1 = -1.0, and using the standard normal distribution table, we find that the area to the left of z1 is 0.1587.

Similarly, assuming z2 = 0.1, the area to the left of z2 is 0.5400.

So, the area between z1 and z2 is 0.5400 - 0.1587 = 0.3813.

To convert this to a percentage, we multiply by 100:
0.3813 * 100 = 38.13%

Therefore, approximately 38.13% of the plants fall between 8 and 11 flowers.