Final answer:
The value of x, where only 20% of the plants are taller, is 17.52 inches. This is found using the z-score for the 80th percentile of a normal distribution and the given mean and standard deviation. So the correct answer is Option A.
Step-by-step explanation:
The student asked to find the value of x for an ornamental plant, where only 20% of the plants are expected to be more than x inches tall, given that the average height is 15 inches with a standard deviation of 3 inches. This is a question of applying the concepts of normal distribution and z-scores in statistics.
Firstly, we must find the z-score that corresponds to the top 20% of the distribution. This is the 80th percentile since 100% - 20% = 80%. Using a z-table or calculator, we find that a z-score of approximately 0.84 corresponds to the 80th percentile. Then, we use the z-score formula:
z = (x - mean) / standard deviation
Plugging in our values:
0.84 = (x - 15) / 3
Now, solve for x:
0.84 * 3 = x - 15
2.52 + 15 = x
x = 17.52 inches
Therefore, only 20% of the plants are expected to be more than 17.52 inches tall.