Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches. Find the probability that one randomly selected fence is under 54 inches.
Z = (score-mean)/SD
Find Z in table in back stats text labeled "areas under normal distribution" to get proportion.
To find the probability that one randomly selected fence is under 54 inches, we can use the standard normal distribution.
First, we need to standardize the measurement using the Z-score formula:
Z = (X - μ) / σ
Where:
X is the given value (54 inches),
μ is the mean (52 inches), and
σ is the standard deviation (4 inches).
Substituting the values into the Z-score formula, we get:
Z = (54 - 52) / 4
Z = 2 / 4
Z = 0.5
Next, we can use a standard normal distribution table (also known as a Z-table) to find the probability corresponding to the Z-score of 0.5.
In the standard normal distribution table, the area to the left of the Z-score (0.5) represents the desired probability.
Looking up the Z-score of 0.5 in the table, we find that the corresponding area is approximately 0.6915.
Therefore, the probability that one randomly selected fence is under 54 inches is approximately 0.6915, or 69.15%.