The height of adult males on a given South Pacific Island is approximately normally distributed with mean 63 inches and standard deviation of 4 inches. What percentage of the adult male population on this island is:
a. Taller than 65
To solve this problem, we need to standardize the height of 65 inches using the formula:
z = (x - μ) / σ
Where:
x = 65 inches (the height we want to find the percentage for)
μ = 63 inches (the mean height of the population)
σ = 4 inches (the standard deviation of the population)
z = (65 - 63) / 4
z = 0.5
Using a standard normal distribution table or calculator, we can find that the percentage of the population taller than 65 inches is about 30.85%.
To find the percentage of the adult male population on the island that is taller than 65 inches, we can use the standard normal distribution.
First, we need to calculate the z-score, which measures how many standard deviations a given value is from the mean:
z = (x - μ) / σ
Where:
x = the given value (65 inches)
μ = the mean (63 inches)
σ = the standard deviation (4 inches)
z = (65 - 63) / 4
z = 2 / 4
z = 0.5
Next, we use a z-table or a calculator to find the percentage of values that are less than the z-score (0.5). This gives us the percentage of the population that is shorter than 65 inches.
Looking up the z-score of 0.5 in a standard normal distribution table or using a calculator, we find that the area to the left of the z-score is approximately 0.6915.
To find the percentage of the population that is taller than 65 inches, we subtract this value from 1:
Percentage = 1 - 0.6915
Percentage = 0.3085
Therefore, approximately 30.85% of the adult male population on this South Pacific Island is taller than 65 inches.