Let
x
represent the full height of certain species of tree. Assume that
x
is normally distributed with a mean of 196.3 feet and a standard deviation of 9.9 feet.
Find the probability that the full height of a randomly selected tree is less than 201.3 feet.
To find the probability that the full height of a randomly selected tree is less than 201.3 feet, we can use the standard normal distribution.
First, we need to standardize the value of 201.3 feet using the formula:
Z = (x - μ) / σ
where:
- Z is the standardized value
- x is the value we want to standardize (201.3 feet in this case)
- μ is the mean (196.3 feet in this case)
- σ is the standard deviation (9.9 feet in this case)
Plugging in the values:
Z = (201.3 - 196.3) / 9.9
Calculating this, we get:
Z ≈ 0.5051
Next, we need to find the probability of a Z-value less than 0.5051 using a standard normal distribution table or a calculator.
Looking up the value 0.5051 in the standard normal distribution table or using a calculator, we find that the corresponding probability is approximately 0.6944.
Therefore, the probability that the full height of a randomly selected tree is less than 201.3 feet is approximately 0.6944 or 69.44%.