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.
To solve this problem, we first need to calculate the Z-scores for the two heights:
Z-score for 20.2 cm: (20.2 - 20) / 3 = 0.067
Z-score for 24.9 cm: (24.9 - 20) / 3 = 1.5
Next, we look up the corresponding probabilities for these Z-scores in a standard normal distribution table.
For a Z-score of 0.067, the probability is 0.5279 (rounded to four decimal places).
For a Z-score of 1.5, the probability is 0.9332.
Now, we calculate the probability that a randomly selected plant is between 20.2 cm and 24.9 cm by finding the difference between these two probabilities:
0.9332 - 0.5279 = 0.4053
Finally, we convert this probability to a percentage:
0.4053 * 100 = 40.53%
Therefore, the probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall is 40.53%.
is this right?
I apologize for the error in my previous response. Let's correct the calculation.
1. Calculate the Z-scores for the two heights:
Z-score for 20.2 cm: (20.2 - 20) / 3 = 0.0667 (approximately)
Z-score for 24.9 cm: (24.9 - 20) / 3 = 1.3
2. Look up the corresponding probabilities for these Z-scores in a standard normal distribution table.
For a Z-score of 0.0667, the probability is approximately 0.5279.
For a Z-score of 1.3, the probability is approximately 0.9032.
3. Calculate the probability that a randomly selected plant is between 20.2 cm and 24.9 cm using the two probabilities:
0.9032 - 0.5279 = 0.3753
4. Convert this probability to a percentage:
0.3753 * 100 = 37.53%
Therefore, the correct probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall is 37.53%. Thank you for pointing out the mistake.