The mean height of a group of plants is 20 centimeters , with a standard deviation of 3 centimeters. What is the probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall? Give the answer as a percentage to the hundredths place ( 1 point ) The probability that a randomly selected plant is between 20.2 and 24.9 centimeters tall
To find the probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall, we need to calculate the z-scores for each of these heights and then find the probability within that range.
First, calculate the z-score for the lower height of 20.2 cm:
z = (x - μ) / σ
z = (20.2 - 20) / 3
z = 0.2 / 3
z = 0.067
Next, calculate the z-score for the higher height of 24.9 cm:
z = (x - μ) / σ
z = (24.9 - 20) / 3
z = 4.9 / 3
z = 1.633
Now, we need to find the area under the standard normal curve between these two z-scores. This can be done using a standard normal distribution table or a calculator. The area between the z-scores of 0.067 and 1.633 is approximately 0.4483.
Therefore, the probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall is 44.83%.