The probability that a sunflower will be less than 115 cm tall is approximately 0.5745.
How to find the probability
To find the probability that a sunflower will be less than 115 cm tall, use the standard normal distribution and z-scores.
First, calculate the z-score for 115 cm using the formula:
z = (x - μ) / σ
where
x is the value we want to find the probability for (115 cm),
μ is the mean (112 cm), and
σ is the standard deviation (16 cm).
z = (115 - 112) / 16
z ≈ 0.1875
Next, use a standard normal distribution table or a statistical calculator to find the probability corresponding to the z-score of 0.1875.
Using a standard normal distribution table, find the cumulative probability associated with the z-score of 0.1875.
The table provides the area to the left of the z-score.
The cumulative probability for a z-score of 0.1875 is approximately 0.5745.
So, the probability that a sunflower will be less than 115 cm tall is approximately 0.5745.
To sketch the area corresponding to this probability, you can draw a normal distribution curve and shade the area to the left of the value 115 cm.
The shaded area represents the probability of a sunflower being less than 115 cm tall.
Attached is the normal distribution curve.